minimal-prime-graphs/MinimalPrimeGraphExamples.py at main · plotnw/minimal-prime-graphs · GitHub

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from sage.graphs.generators.basic import CycleGraph
from sage.graphs.graph import Graph
# Define some simple examples

C5 = CycleGraph(5)

# The following graph is Figure 6 in Florez et al. Minimal Prime Graphs of Finite Solvable Groups
# It is given as an example of a non-reseminant minimal prime graph
# However, NR8 is not a prime graph itself, so while it passes the edge removal test, it is not a minimal prime graph
# Since the complement already has a triangle adding any edge to the complement will automatically fail that edge
# So ultimately doesn't mean a lot
# One triangle in the complement is between vertices 0, 5, 6. There might be others
NR8 = Graph(
    {0: [1, 7],
     1: [0, 2],
     2: [1, 3],
     3: [1, 2, 4, 5, 6],
     4: [3, 5, 6, 7],
     5: [1, 3, 4, 7],
     6: [3, 4, 7],
     7: [0, 4, 5, 6]})

NR8.set_pos(
    {0: (0, 2),
     1: (1, 2),
     2: (2, 2),
     3: (1.7, 1.5),
     4: (1, .8),
     5: (1.35, 1),
     6: (2, 0),
     7: (0, 1)})


# Define all examples with between 5 and 10 vertices
# Generated through `GenerateMinimalPrimeGraphs.py`
MPG_5_0 = Graph({0: [2, 3], 1: [3, 4], 2: [0, 4], 3: [0, 1], 4: [1, 2]})
MPG_5_0.name("MPG_5_0")

MPGS_5 = [MPG_5_0]

MPG_6_0 = Graph({0: [2, 3, 5], 1: [3, 4, 5], 2: [0, 4], 3: [0, 1, 5], 4: [1, 2], 5: [0, 1, 3]})
MPG_6_0.name("MPG_6_0")

MPGS_6 = [MPG_6_0]

MPG_7_0 = Graph({0: [2, 4, 5], 1: [3, 5, 6], 2: [0, 4, 6], 3: [1, 5, 6], 4: [0, 2, 6], 5: [0, 1, 3], 6: [1, 2, 3, 4]})
MPG_7_1 = Graph({0: [2, 4, 5, 6], 1: [3, 4], 2: [0, 4, 5, 6], 3: [1, 5], 4: [0, 1, 2, 6], 5: [0, 2, 3, 6], 6: [0, 2, 4, 5]})
MPG_7_2 = Graph({0: [2, 4, 5, 6], 1: [3, 4, 6], 2: [0, 4, 5, 6], 3: [1, 5], 4: [0, 1, 2, 6], 5: [0, 2, 3], 6: [0, 1, 2, 4]})
MPG_7_0.name("MPG_7_0")
MPG_7_1.name("MPG_7_1")
MPG_7_2.name("MPG_7_2")

MPGS_7 = [MPG_7_0, MPG_7_1, MPG_7_2]

MPG_8_0 = Graph({0: [2, 4, 6, 7], 1: [3, 5, 6], 2: [0, 4, 6, 7], 3: [1, 5, 7], 4: [0, 2, 6, 7], 5: [1, 3, 7], 6: [0, 1, 2, 4], 7: [0, 2, 3, 4, 5]})
MPG_8_1 = Graph({0: [2, 4, 5], 1: [3, 5, 6, 7], 2: [0, 4, 6, 7], 3: [1, 5, 6, 7], 4: [0, 2, 6, 7], 5: [0, 1, 3], 6: [1, 2, 3, 4, 7], 7: [1, 2, 3, 4, 6]})
MPG_8_2 = Graph({0: [2, 4, 5, 7], 1: [3, 5, 6, 7], 2: [0, 4, 6], 3: [1, 5, 6, 7], 4: [0, 2, 6], 5: [0, 1, 3, 7], 6: [1, 2, 3, 4], 7: [0, 1, 3, 5]})
MPG_8_3 = Graph({0: [2, 4, 5, 6, 7], 1: [3, 5], 2: [0, 4, 5, 6, 7], 3: [1, 6], 4: [0, 2, 5, 6, 7], 5: [0, 1, 2, 4, 7], 6: [0, 2, 3, 4, 7], 7: [0, 2, 4, 5, 6]})
MPG_8_4 = Graph({0: [2, 4, 5, 6, 7], 1: [3, 5, 7], 2: [0, 4, 5, 6, 7], 3: [1, 6], 4: [0, 2, 5, 6, 7], 5: [0, 1, 2, 4, 7], 6: [0, 2, 3, 4], 7: [0, 1, 2, 4, 5]})
MPG_8_5 = Graph({0: [2, 4, 5, 6], 1: [3, 4, 6, 7], 2: [0, 4, 5, 7], 3: [1, 5, 6, 7], 4: [0, 1, 2, 6], 5: [0, 2, 3, 7], 6: [0, 1, 3, 4], 7: [1, 2, 3, 5]})
MPG_8_0.name("MPG_8_0")
MPG_8_1.name("MPG_8_1")
MPG_8_2.name("MPG_8_2")
MPG_8_3.name("MPG_8_3")
MPG_8_4.name("MPG_8_4")
MPG_8_5.name("MPG_8_5")

MPGS_8 = [MPG_8_0, MPG_8_1, MPG_8_2, MPG_8_3, MPG_8_4, MPG_8_5]

MPG_9_0 = Graph({0: [2, 4, 6, 7], 1: [3, 5, 7, 8], 2: [0, 4, 6, 8], 3: [1, 5, 7, 8], 4: [0, 2, 6, 8], 5: [1, 3, 7, 8], 6: [0, 2, 4, 8], 7: [0, 1, 3, 5], 8: [1, 2, 3, 4, 5, 6]})
MPG_9_1 = Graph({0: [2, 4, 6, 7, 8], 1: [3, 5, 7], 2: [0, 4, 6, 7, 8], 3: [1, 5, 8], 4: [0, 2, 6, 7, 8], 5: [1, 3, 8], 6: [0, 2, 4, 7, 8], 7: [0, 1, 2, 4, 6], 8: [0, 2, 3, 4, 5, 6]})
MPG_9_2 = Graph({0: [2, 4, 6, 7], 1: [3, 5, 7, 8], 2: [0, 4, 6, 7], 3: [1, 5, 7, 8], 4: [0, 2, 6, 8], 5: [1, 3, 7, 8], 6: [0, 2, 4, 8], 7: [0, 1, 2, 3, 5], 8: [1, 3, 4, 5, 6]})
MPG_9_3 = Graph({0: [2, 4, 6, 7, 8], 1: [3, 5, 6], 2: [0, 4, 6, 7, 8], 3: [1, 5, 7, 8], 4: [0, 2, 6, 7, 8], 5: [1, 3, 7, 8], 6: [0, 1, 2, 4], 7: [0, 2, 3, 4, 5, 8], 8: [0, 2, 3, 4, 5, 7]})
MPG_9_4 = Graph({0: [2, 4, 5, 6, 7, 8], 1: [3, 6], 2: [0, 4, 5, 6, 7, 8], 3: [1, 7], 4: [0, 2, 5, 6, 7, 8], 5: [0, 2, 4, 6, 7, 8], 6: [0, 1, 2, 4, 5, 8], 7: [0, 2, 3, 4, 5, 8], 8: [0, 2, 4, 5, 6, 7]})
MPG_9_5 = Graph({0: [2, 4, 5, 6, 7, 8], 1: [3, 6, 8], 2: [0, 4, 5, 6, 7, 8], 3: [1, 7], 4: [0, 2, 5, 6, 7, 8], 5: [0, 2, 4, 6, 7, 8], 6: [0, 1, 2, 4, 5, 8], 7: [0, 2, 3, 4, 5], 8: [0, 1, 2, 4, 5, 6]})
MPG_9_6 = Graph({0: [2, 4, 5], 1: [3, 5, 6, 7, 8], 2: [0, 4, 6, 7, 8], 3: [1, 5, 6, 7, 8], 4: [0, 2, 6, 7, 8], 5: [0, 1, 3], 6: [1, 2, 3, 4, 7, 8], 7: [1, 2, 3, 4, 6, 8], 8: [1, 2, 3, 4, 6, 7]})
MPG_9_7 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 5, 6, 7], 2: [0, 4, 7, 8], 3: [1, 5, 6, 7], 4: [0, 2, 7, 8], 5: [0, 1, 3, 6, 8], 6: [0, 1, 3, 5, 8], 7: [1, 2, 3, 4], 8: [0, 2, 4, 5, 6]})
MPG_9_8 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 5, 6, 7, 8], 2: [0, 4, 7], 3: [1, 5, 6, 7, 8], 4: [0, 2, 7], 5: [0, 1, 3, 6, 8], 6: [0, 1, 3, 5, 8], 7: [1, 2, 3, 4], 8: [0, 1, 3, 5, 6]})
MPG_9_9 = Graph({0: [2, 4, 5, 6, 7, 8], 1: [3, 5, 7, 8], 2: [0, 4, 5, 6, 7, 8], 3: [1, 6], 4: [0, 2, 5, 6, 7, 8], 5: [0, 1, 2, 4, 7, 8], 6: [0, 2, 3, 4], 7: [0, 1, 2, 4, 5, 8], 8: [0, 1, 2, 4, 5, 7]})
MPG_9_10 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 4, 6, 7, 8], 2: [0, 4, 5, 7, 8], 3: [1, 5, 6, 7], 4: [0, 1, 2, 6, 8], 5: [0, 2, 3, 7], 6: [0, 1, 3, 4, 8], 7: [1, 2, 3, 5], 8: [0, 1, 2, 4, 6]})
MPG_9_11 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 4, 6, 7, 8], 2: [0, 4, 5, 7], 3: [1, 5, 6, 7, 8], 4: [0, 1, 2, 6, 7], 5: [0, 2, 3, 7, 8], 6: [0, 1, 3, 4, 8], 7: [1, 2, 3, 4, 5], 8: [0, 1, 3, 5, 6]})
MPG_9_0.name("MPG_9_0")
MPG_9_1.name("MPG_9_1")
MPG_9_2.name("MPG_9_2")
MPG_9_3.name("MPG_9_3")
MPG_9_4.name("MPG_9_4")
MPG_9_5.name("MPG_9_5")
MPG_9_6.name("MPG_9_6")
MPG_9_7.name("MPG_9_7")
MPG_9_8.name("MPG_9_8")
MPG_9_9.name("MPG_9_9")
MPG_9_10.name("MPG_9_10")
MPG_9_11.name("MPG_9_11")

MPGS_9 = [MPG_9_0, MPG_9_1, MPG_9_2, MPG_9_3, MPG_9_4, MPG_9_5, MPG_9_6, MPG_9_7, MPG_9_8, MPG_9_9, MPG_9_10, MPG_9_11]

MPG_10_0 = Graph({0: [2, 4, 6, 8, 9], 1: [3, 5, 7, 8], 2: [0, 4, 6, 8, 9], 3: [1, 5, 7, 9], 4: [0, 2, 6, 8, 9], 5: [1, 3, 7, 9], 6: [0, 2, 4, 8, 9], 7: [1, 3, 5, 9], 8: [0, 1, 2, 4, 6], 9: [0, 2, 3, 4, 5, 6, 7]})
MPG_10_1 = Graph({0: [2, 4, 6, 8, 9], 1: [3, 5, 7, 8], 2: [0, 4, 6, 8, 9], 3: [1, 5, 7, 8], 4: [0, 2, 6, 8, 9], 5: [1, 3, 7, 9], 6: [0, 2, 4, 8, 9], 7: [1, 3, 5, 9], 8: [0, 1, 2, 3, 4, 6], 9: [0, 2, 4, 5, 6, 7]})
MPG_10_2 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 8], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 9], 4: [0, 2, 6, 7, 8, 9], 5: [1, 3, 9], 6: [0, 2, 4, 7, 8, 9], 7: [0, 2, 4, 6, 8, 9], 8: [0, 1, 2, 4, 6, 7], 9: [0, 2, 3, 4, 5, 6, 7]})
MPG_10_3 = Graph({0: [2, 4, 6, 7], 1: [3, 5, 7, 8, 9], 2: [0, 4, 6, 8, 9], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 8, 9], 5: [1, 3, 7, 8, 9], 6: [0, 2, 4, 8, 9], 7: [0, 1, 3, 5], 8: [1, 2, 3, 4, 5, 6, 9], 9: [1, 2, 3, 4, 5, 6, 8]})
MPG_10_4 = Graph({0: [2, 4, 6, 7, 8], 1: [3, 5, 7, 8, 9], 2: [0, 4, 6, 9], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 9], 5: [1, 3, 7, 8, 9], 6: [0, 2, 4, 9], 7: [0, 1, 3, 5, 8], 8: [0, 1, 3, 5, 7], 9: [1, 2, 3, 4, 5, 6]})
MPG_10_5 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 7], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 8, 9], 4: [0, 2, 6, 7, 8, 9], 5: [1, 3, 8, 9], 6: [0, 2, 4, 7, 8, 9], 7: [0, 1, 2, 4, 6], 8: [0, 2, 3, 4, 5, 6, 9], 9: [0, 2, 3, 4, 5, 6, 8]})
MPG_10_6 = Graph({0: [2, 4, 6, 7, 9], 1: [3, 5, 7, 8, 9], 2: [0, 4, 6, 7, 9], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 8], 5: [1, 3, 7, 8, 9], 6: [0, 2, 4, 8], 7: [0, 1, 2, 3, 5, 9], 8: [1, 3, 4, 5, 6], 9: [0, 1, 2, 3, 5, 7]})
MPG_10_7 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 6], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 7, 8, 9], 5: [1, 3, 7, 8, 9], 6: [0, 1, 2, 4], 7: [0, 2, 3, 4, 5, 8, 9], 8: [0, 2, 3, 4, 5, 7, 9], 9: [0, 2, 3, 4, 5, 7, 8]})
MPG_10_8 = Graph({0: [2, 4, 6, 7, 9], 1: [3, 5, 6, 7, 8], 2: [0, 4, 6, 8, 9], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 8, 9], 5: [1, 3, 7, 8, 9], 6: [0, 1, 2, 4, 8], 7: [0, 1, 3, 5, 9], 8: [1, 2, 3, 4, 5, 6], 9: [0, 2, 3, 4, 5, 7]})
MPG_10_9 = Graph({0: [2, 4, 6, 7, 8], 1: [3, 5, 6, 7, 9], 2: [0, 4, 6, 8, 9], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 8, 9], 5: [1, 3, 7, 8, 9], 6: [0, 1, 2, 4, 7], 7: [0, 1, 3, 5, 6], 8: [0, 2, 3, 4, 5, 9], 9: [1, 2, 3, 4, 5, 8]})
MPG_10_10 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 6, 7], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 8], 4: [0, 2, 6, 7, 8, 9], 5: [1, 3, 8], 6: [0, 1, 2, 4, 7, 9], 7: [0, 1, 2, 4, 6, 9], 8: [0, 2, 3, 4, 5, 9], 9: [0, 2, 4, 6, 7, 8]})
MPG_10_11 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 6, 7, 9], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 8], 4: [0, 2, 6, 7, 8, 9], 5: [1, 3, 8], 6: [0, 1, 2, 4, 7, 9], 7: [0, 1, 2, 4, 6, 9], 8: [0, 2, 3, 4, 5], 9: [0, 1, 2, 4, 6, 7]})
MPG_10_12 = Graph({0: [2, 4, 5, 6, 7, 8, 9], 1: [3, 7], 2: [0, 4, 5, 6, 7, 8, 9], 3: [1, 8], 4: [0, 2, 5, 6, 7, 8, 9], 5: [0, 2, 4, 6, 7, 8, 9], 6: [0, 2, 4, 5, 7, 8, 9], 7: [0, 1, 2, 4, 5, 6, 9], 8: [0, 2, 3, 4, 5, 6, 9], 9: [0, 2, 4, 5, 6, 7, 8]})
MPG_10_13 = Graph({0: [2, 4, 5, 6, 7, 8, 9], 1: [3, 7, 9], 2: [0, 4, 5, 6, 7, 8, 9], 3: [1, 8], 4: [0, 2, 5, 6, 7, 8, 9], 5: [0, 2, 4, 6, 7, 8, 9], 6: [0, 2, 4, 5, 7, 8, 9], 7: [0, 1, 2, 4, 5, 6, 9], 8: [0, 2, 3, 4, 5, 6], 9: [0, 1, 2, 4, 5, 6, 7]})
MPG_10_14 = Graph({0: [2, 4, 5, 6, 7, 8, 9], 1: [3, 6, 8, 9], 2: [0, 4, 5, 6, 7, 8, 9], 3: [1, 7], 4: [0, 2, 5, 6, 7, 8, 9], 5: [0, 2, 4, 6, 7, 8, 9], 6: [0, 1, 2, 4, 5, 8, 9], 7: [0, 2, 3, 4, 5], 8: [0, 1, 2, 4, 5, 6, 9], 9: [0, 1, 2, 4, 5, 6, 8]})
MPG_10_15 = Graph({0: [2, 4, 5], 1: [3, 5, 6, 7, 8, 9], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 6, 7, 8, 9], 4: [0, 2, 6, 7, 8, 9], 5: [0, 1, 3], 6: [1, 2, 3, 4, 7, 8, 9], 7: [1, 2, 3, 4, 6, 8, 9], 8: [1, 2, 3, 4, 6, 7, 9], 9: [1, 2, 3, 4, 6, 7, 8]})
MPG_10_16 = Graph({0: [2, 4, 5, 7, 8], 1: [3, 5, 6, 7, 9], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 6, 8, 9], 4: [0, 2, 6, 7, 8, 9], 5: [0, 1, 3, 8], 6: [1, 2, 3, 4, 7, 9], 7: [0, 1, 2, 4, 6, 9], 8: [0, 2, 3, 4, 5], 9: [1, 2, 3, 4, 6, 7]})
MPG_10_17 = Graph({0: [2, 4, 5, 7, 8, 9], 1: [3, 5, 6, 7], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 6, 8], 4: [0, 2, 6, 7, 8, 9], 5: [0, 1, 3, 8], 6: [1, 2, 3, 4, 7, 9], 7: [0, 1, 2, 4, 6, 9], 8: [0, 2, 3, 4, 5, 9], 9: [0, 2, 4, 6, 7, 8]})
MPG_10_18 = Graph({0: [2, 4, 5, 7, 8, 9], 1: [3, 5, 6, 7, 9], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 6, 8], 4: [0, 2, 6, 7, 8, 9], 5: [0, 1, 3, 8], 6: [1, 2, 3, 4, 7, 9], 7: [0, 1, 2, 4, 6, 9], 8: [0, 2, 3, 4, 5], 9: [0, 1, 2, 4, 6, 7]})
MPG_10_19 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 5, 6, 7, 9], 2: [0, 4, 7, 8, 9], 3: [1, 5, 6, 7, 9], 4: [0, 2, 7, 8, 9], 5: [0, 1, 3, 6, 8], 6: [0, 1, 3, 5, 8], 7: [1, 2, 3, 4, 9], 8: [0, 2, 4, 5, 6], 9: [1, 2, 3, 4, 7]})
MPG_10_20 = Graph({0: [2, 4, 5, 6, 8, 9], 1: [3, 5, 6, 7, 9], 2: [0, 4, 7, 8], 3: [1, 5, 6, 7, 9], 4: [0, 2, 7, 8], 5: [0, 1, 3, 6, 8, 9], 6: [0, 1, 3, 5, 8, 9], 7: [1, 2, 3, 4], 8: [0, 2, 4, 5, 6, 9], 9: [0, 1, 3, 5, 6, 8]})
MPG_10_21 = Graph({0: [2, 4, 5, 6, 8, 9], 1: [3, 5, 6, 7, 8], 2: [0, 4, 7, 8, 9], 3: [1, 5, 6, 7, 9], 4: [0, 2, 7, 8, 9], 5: [0, 1, 3, 6, 8], 6: [0, 1, 3, 5, 9], 7: [1, 2, 3, 4, 8, 9], 8: [0, 1, 2, 4, 5, 7], 9: [0, 2, 3, 4, 6, 7]})
MPG_10_22 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 4, 6, 7, 8, 9], 2: [0, 4, 5, 7, 9], 3: [1, 5, 6, 7, 8, 9], 4: [0, 1, 2, 6, 7, 9], 5: [0, 2, 3, 7, 8], 6: [0, 1, 3, 4, 8, 9], 7: [1, 2, 3, 4, 5, 9], 8: [0, 1, 3, 5, 6], 9: [1, 2, 3, 4, 6, 7]})
MPG_10_23 = Graph({0: [2, 4, 5, 6, 8], 1: [3, 4, 6, 7, 8, 9], 2: [0, 4, 5, 7, 9], 3: [1, 5, 6, 7, 8, 9], 4: [0, 1, 2, 6, 7, 9], 5: [0, 2, 3, 7, 8, 9], 6: [0, 1, 3, 4, 8], 7: [1, 2, 3, 4, 5, 9], 8: [0, 1, 3, 5, 6], 9: [1, 2, 3, 4, 5, 7]})
MPG_10_24 = Graph({0: [2, 4, 5, 6, 8, 9], 1: [3, 4, 6, 7, 8, 9], 2: [0, 4, 5, 7], 3: [1, 5, 6, 7, 8, 9], 4: [0, 1, 2, 6, 7, 9], 5: [0, 2, 3, 7, 8], 6: [0, 1, 3, 4, 8, 9], 7: [1, 2, 3, 4, 5], 8: [0, 1, 3, 5, 6, 9], 9: [0, 1, 3, 4, 6, 8]})
MPG_10_25 = Graph({0: [2, 3, 5, 6, 8, 9], 1: [3, 4, 5, 6, 7, 8], 2: [0, 4, 5, 7, 8, 9], 3: [0, 1, 5, 6, 7, 9], 4: [1, 2, 6, 7, 8, 9], 5: [0, 1, 2, 3, 7, 8], 6: [0, 1, 3, 4, 8, 9], 7: [1, 2, 3, 4, 5, 9], 8: [0, 1, 2, 4, 5, 6], 9: [0, 2, 3, 4, 6, 7]})
MPG_10_0.name("MPG_10_0")
MPG_10_1.name("MPG_10_1")
MPG_10_2.name("MPG_10_2")
MPG_10_3.name("MPG_10_3")
MPG_10_4.name("MPG_10_4")
MPG_10_5.name("MPG_10_5")
MPG_10_6.name("MPG_10_6")
MPG_10_7.name("MPG_10_7")
MPG_10_8.name("MPG_10_8")
MPG_10_9.name("MPG_10_9")
MPG_10_10.name("MPG_10_10")
MPG_10_11.name("MPG_10_11")
MPG_10_12.name("MPG_10_12")
MPG_10_13.name("MPG_10_13")
MPG_10_14.name("MPG_10_14")
MPG_10_15.name("MPG_10_15")
MPG_10_16.name("MPG_10_16")
MPG_10_17.name("MPG_10_17")
MPG_10_18.name("MPG_10_18")
MPG_10_19.name("MPG_10_19")
MPG_10_20.name("MPG_10_20")
MPG_10_21.name("MPG_10_21")
MPG_10_22.name("MPG_10_22")
MPG_10_23.name("MPG_10_23")
MPG_10_24.name("MPG_10_24")
MPG_10_25.name("MPG_10_25")

MPGS_10 = [MPG_10_0, MPG_10_1, MPG_10_2, MPG_10_3, MPG_10_4, MPG_10_5, MPG_10_6, MPG_10_7, MPG_10_8, MPG_10_9, MPG_10_10, MPG_10_11, MPG_10_12, MPG_10_13, MPG_10_14, MPG_10_15, MPG_10_16, MPG_10_17, MPG_10_18, MPG_10_19, MPG_10_20, MPG_10_21, MPG_10_22, MPG_10_23, MPG_10_24, MPG_10_25]

MPG_11_0 = Graph({0: [2, 4, 6, 8, 9], 1: [3, 5, 7, 9, 10], 2: [0, 4, 6, 8, 10], 3: [1, 5, 7, 9, 10], 4: [0, 2, 6, 8, 10], 5: [1, 3, 7, 9, 10], 6: [0, 2, 4, 8, 10], 7: [1, 3, 5, 9, 10], 8: [0, 2, 4, 6, 10], 9: [0, 1, 3, 5, 7], 10: [1, 2, 3, 4, 5, 6, 7, 8]})
MPG_11_1 = Graph({0: [2, 4, 6, 8, 9], 1: [3, 5, 7, 9, 10], 2: [0, 4, 6, 8, 9], 3: [1, 5, 7, 9, 10], 4: [0, 2, 6, 8, 10], 5: [1, 3, 7, 9, 10], 6: [0, 2, 4, 8, 10], 7: [1, 3, 5, 9, 10], 8: [0, 2, 4, 6, 10], 9: [0, 1, 2, 3, 5, 7], 10: [1, 3, 4, 5, 6, 7, 8]})
MPG_11_2 = Graph({0: [2, 4, 6, 8, 9, 10], 1: [3, 5, 7, 9], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 10], 6: [0, 2, 4, 8, 9, 10], 7: [1, 3, 5, 10], 8: [0, 2, 4, 6, 9, 10], 9: [0, 1, 2, 4, 6, 8], 10: [0, 2, 3, 4, 5, 6, 7, 8]})
MPG_11_3 = Graph({0: [2, 4, 6, 8, 9, 10], 1: [3, 5, 7, 9], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 9], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 10], 6: [0, 2, 4, 8, 9, 10], 7: [1, 3, 5, 10], 8: [0, 2, 4, 6, 9, 10], 9: [0, 1, 2, 3, 4, 6, 8], 10: [0, 2, 4, 5, 6, 7, 8]})
MPG_11_4 = Graph({0: [2, 4, 6, 8, 9, 10], 1: [3, 5, 7, 8, 9], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 10], 6: [0, 2, 4, 8, 9, 10], 7: [1, 3, 5, 10], 8: [0, 1, 2, 4, 6, 9], 9: [0, 1, 2, 4, 6, 8], 10: [0, 2, 3, 4, 5, 6, 7]})
MPG_11_5 = Graph({0: [2, 4, 6, 7, 8, 10], 1: [3, 5, 7, 8, 9, 10], 2: [0, 4, 6, 9], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 9], 5: [1, 3, 7, 8, 9, 10], 6: [0, 2, 4, 9], 7: [0, 1, 3, 5, 8, 10], 8: [0, 1, 3, 5, 7, 10], 9: [1, 2, 3, 4, 5, 6], 10: [0, 1, 3, 5, 7, 8]})
MPG_11_6 = Graph({0: [2, 4, 6, 7, 8, 10], 1: [3, 5, 7, 8, 9], 2: [0, 4, 6, 9, 10], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 9, 10], 5: [1, 3, 7, 8, 9], 6: [0, 2, 4, 9, 10], 7: [0, 1, 3, 5, 8, 10], 8: [0, 1, 3, 5, 7, 10], 9: [1, 2, 3, 4, 5, 6], 10: [0, 2, 4, 6, 7, 8]})
MPG_11_7 = Graph({0: [2, 4, 6, 8, 9, 10], 1: [3, 5, 7, 8, 10], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 9], 6: [0, 2, 4, 8, 9, 10], 7: [1, 3, 5, 9], 8: [0, 1, 2, 3, 4, 6, 10], 9: [0, 2, 4, 5, 6, 7], 10: [0, 1, 2, 3, 4, 6, 8]})
MPG_11_8 = Graph({0: [2, 4, 6, 7, 8], 1: [3, 5, 7, 8, 9, 10], 2: [0, 4, 6, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 2, 4, 9, 10], 7: [0, 1, 3, 5, 8], 8: [0, 1, 3, 5, 7], 9: [1, 2, 3, 4, 5, 6, 10], 10: [1, 2, 3, 4, 5, 6, 9]})
MPG_11_9 = Graph({0: [2, 4, 5, 6, 8, 10], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 7, 8, 9], 3: [1, 5, 6, 7, 9, 10], 4: [0, 2, 7, 8, 9], 5: [0, 1, 3, 6, 8, 10], 6: [0, 1, 3, 5, 8, 10], 7: [1, 2, 3, 4, 9], 8: [0, 2, 4, 5, 6, 10], 9: [1, 2, 3, 4, 7], 10: [0, 1, 3, 5, 6, 8]})
MPG_11_10 = Graph({0: [2, 4, 6, 8, 9, 10], 1: [3, 5, 7, 8], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 9, 10], 6: [0, 2, 4, 8, 9, 10], 7: [1, 3, 5, 9, 10], 8: [0, 1, 2, 4, 6], 9: [0, 2, 3, 4, 5, 6, 7, 10], 10: [0, 2, 3, 4, 5, 6, 7, 9]})
MPG_11_11 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 7, 8, 10], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 9, 10], 6: [0, 2, 4, 8, 9, 10], 7: [0, 1, 3, 5, 9], 8: [0, 1, 2, 4, 6, 10], 9: [0, 2, 3, 4, 5, 6, 7], 10: [1, 2, 3, 4, 5, 6, 8]})
MPG_11_12 = Graph({0: [2, 4, 6, 7, 8], 1: [3, 5, 7, 8, 9, 10], 2: [0, 4, 6, 8, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 2, 4, 9, 10], 7: [0, 1, 3, 5, 8, 9], 8: [0, 1, 2, 3, 5, 7], 9: [1, 3, 4, 5, 6, 7, 10], 10: [1, 2, 3, 4, 5, 6, 9]})
MPG_11_13 = Graph({0: [2, 4, 6, 7, 9, 10], 1: [3, 5, 7, 8, 9, 10], 2: [0, 4, 6, 7, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8], 5: [1, 3, 7, 8, 9, 10], 6: [0, 2, 4, 8], 7: [0, 1, 2, 3, 5, 9, 10], 8: [1, 3, 4, 5, 6], 9: [0, 1, 2, 3, 5, 7, 10], 10: [0, 1, 2, 3, 5, 7, 9]})
MPG_11_14 = Graph({0: [2, 4, 6, 7, 9, 10], 1: [3, 5, 7, 8, 9], 2: [0, 4, 6, 7, 9, 10], 3: [1, 5, 7, 8, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 10], 6: [0, 2, 4, 8, 9, 10], 7: [0, 1, 2, 3, 5, 9], 8: [1, 3, 4, 5, 6, 10], 9: [0, 1, 2, 4, 6, 7], 10: [0, 2, 3, 4, 5, 6, 8]})
MPG_11_15 = Graph({0: [2, 4, 6, 7, 8, 10], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 9], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 9], 6: [0, 1, 2, 4, 7, 10], 7: [0, 1, 3, 5, 6, 10], 8: [0, 2, 3, 4, 5, 9], 9: [1, 2, 3, 4, 5, 8], 10: [0, 1, 2, 4, 6, 7]})
MPG_11_16 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 9], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 10], 6: [0, 2, 4, 7, 8, 9, 10], 7: [0, 2, 4, 6, 8, 9, 10], 8: [0, 2, 4, 6, 7, 9, 10], 9: [0, 1, 2, 4, 6, 7, 8], 10: [0, 2, 3, 4, 5, 6, 7, 8]})
MPG_11_17 = Graph({0: [2, 4, 6, 7, 9], 1: [3, 5, 7, 8, 9, 10], 2: [0, 4, 6, 7, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8, 9], 5: [1, 3, 7, 8, 9, 10], 6: [0, 2, 4, 8, 10], 7: [0, 1, 2, 3, 5, 9, 10], 8: [1, 3, 4, 5, 6, 9, 10], 9: [0, 1, 3, 4, 5, 7, 8], 10: [1, 2, 3, 5, 6, 7, 8]})
MPG_11_18 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 7, 8, 10], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 9], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 9], 6: [0, 2, 4, 7, 8, 9, 10], 7: [0, 1, 2, 4, 6, 8, 10], 8: [0, 1, 2, 4, 6, 7, 10], 9: [0, 2, 3, 4, 5, 6], 10: [0, 1, 2, 4, 6, 7, 8]})
MPG_11_19 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 7, 8], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 9], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 9], 6: [0, 2, 4, 7, 8, 9, 10], 7: [0, 1, 2, 4, 6, 8, 10], 8: [0, 1, 2, 4, 6, 7, 10], 9: [0, 2, 3, 4, 5, 6, 10], 10: [0, 2, 4, 6, 7, 8, 9]})
MPG_11_20 = Graph({0: [2, 4, 6, 7, 9], 1: [3, 5, 6, 7, 8, 10], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 1, 2, 4, 8, 10], 7: [0, 1, 3, 5, 9], 8: [1, 2, 3, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7], 10: [1, 2, 3, 4, 5, 6, 8]})
MPG_11_21 = Graph({0: [2, 4, 6, 7, 9, 10], 1: [3, 5, 6, 7, 8, 9], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 10], 6: [0, 1, 2, 4, 8, 9], 7: [0, 1, 3, 5, 9, 10], 8: [1, 2, 3, 4, 5, 6, 10], 9: [0, 1, 2, 4, 6, 7], 10: [0, 2, 3, 4, 5, 7, 8]})
MPG_11_22 = Graph({0: [2, 4, 6, 7, 8, 9], 1: [3, 5, 6, 7, 10], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 1, 2, 4, 7], 7: [0, 1, 3, 5, 6], 8: [0, 2, 3, 4, 5, 9, 10], 9: [0, 2, 3, 4, 5, 8, 10], 10: [1, 2, 3, 4, 5, 8, 9]})
MPG_11_23 = Graph({0: [2, 4, 5, 7, 8, 10], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 6, 7, 8, 9], 3: [1, 5, 6, 8, 9, 10], 4: [0, 2, 6, 7, 8, 10], 5: [0, 1, 3, 8, 9, 10], 6: [1, 2, 3, 4, 7, 9], 7: [0, 1, 2, 4, 6, 9], 8: [0, 2, 3, 4, 5, 10], 9: [1, 2, 3, 5, 6, 7], 10: [0, 1, 3, 4, 5, 8]})
MPG_11_24 = Graph({0: [2, 4, 5, 6, 8, 9, 10], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 7, 8], 3: [1, 5, 6, 7, 9, 10], 4: [0, 2, 7, 8], 5: [0, 1, 3, 6, 8, 9, 10], 6: [0, 1, 3, 5, 8, 9, 10], 7: [1, 2, 3, 4], 8: [0, 2, 4, 5, 6, 9, 10], 9: [0, 1, 3, 5, 6, 8, 10], 10: [0, 1, 3, 5, 6, 8, 9]})
MPG_11_25 = Graph({0: [2, 4, 5, 6, 8, 9, 10], 1: [3, 5, 6, 7, 9], 2: [0, 4, 7, 8, 10], 3: [1, 5, 6, 7, 9], 4: [0, 2, 7, 8, 10], 5: [0, 1, 3, 6, 8, 9, 10], 6: [0, 1, 3, 5, 8, 9, 10], 7: [1, 2, 3, 4], 8: [0, 2, 4, 5, 6, 9, 10], 9: [0, 1, 3, 5, 6, 8, 10], 10: [0, 2, 4, 5, 6, 8, 9]})
MPG_11_26 = Graph({0: [2, 4, 6, 7], 1: [3, 5, 7, 8, 9, 10], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 2, 4, 8, 9, 10], 7: [0, 1, 3, 5], 8: [1, 2, 3, 4, 5, 6, 9, 10], 9: [1, 2, 3, 4, 5, 6, 8, 10], 10: [1, 2, 3, 4, 5, 6, 8, 9]})
MPG_11_27 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 8], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 9, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 9, 10], 6: [0, 2, 4, 7, 8, 9, 10], 7: [0, 2, 4, 6, 8, 9, 10], 8: [0, 1, 2, 4, 6, 7], 9: [0, 2, 3, 4, 5, 6, 7, 10], 10: [0, 2, 3, 4, 5, 6, 7, 9]})
MPG_11_28 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 6, 8, 10], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 7, 9], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 8, 9, 10], 6: [0, 1, 2, 4, 7, 8, 10], 7: [0, 2, 3, 4, 6, 9], 8: [0, 1, 2, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7], 10: [0, 1, 2, 4, 5, 6, 8]})
MPG_11_29 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 6, 8, 10], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 7, 9], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 8, 9], 6: [0, 1, 2, 4, 7, 8, 10], 7: [0, 2, 3, 4, 6, 9, 10], 8: [0, 1, 2, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7], 10: [0, 1, 2, 4, 6, 7, 8]})
MPG_11_30 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 6, 8], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 7, 9], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 8, 9], 6: [0, 1, 2, 4, 7, 8, 10], 7: [0, 2, 3, 4, 6, 9, 10], 8: [0, 1, 2, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7, 10], 10: [0, 2, 4, 6, 7, 8, 9]})
MPG_11_31 = Graph({0: [2, 4, 6, 7, 9, 10], 1: [3, 5, 6, 7, 8], 2: [0, 4, 6, 8, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 1, 2, 4, 7, 8], 7: [0, 1, 3, 5, 6, 9], 8: [1, 2, 3, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7, 10], 10: [0, 2, 3, 4, 5, 8, 9]})
MPG_11_32 = Graph({0: [2, 4, 5, 6, 8, 9], 1: [3, 5, 6, 7, 8, 10], 2: [0, 4, 6, 7, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 8, 9, 10], 5: [0, 1, 3, 7, 8, 9], 6: [0, 1, 2, 4, 8, 10], 7: [1, 2, 3, 5, 9, 10], 8: [0, 1, 3, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7], 10: [1, 2, 3, 4, 6, 7, 8]})
MPG_11_33 = Graph({0: [2, 4, 5, 6, 8, 9], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 7, 8, 9, 10], 3: [1, 5, 6, 7, 9, 10], 4: [0, 2, 7, 8, 9, 10], 5: [0, 1, 3, 6, 8, 9], 6: [0, 1, 3, 5, 8, 10], 7: [1, 2, 3, 4, 9, 10], 8: [0, 2, 4, 5, 6, 10], 9: [0, 1, 2, 3, 4, 5, 7], 10: [1, 2, 3, 4, 6, 7, 8]})
MPG_11_34 = Graph({0: [2, 4, 5, 6, 8, 10], 1: [3, 5, 6, 7, 8, 9, 10], 2: [0, 4, 7, 8, 10], 3: [1, 5, 6, 7, 8, 9, 10], 4: [0, 2, 7, 9], 5: [0, 1, 3, 6, 8, 9, 10], 6: [0, 1, 3, 5, 8, 9, 10], 7: [1, 2, 3, 4, 9], 8: [0, 1, 2, 3, 5, 6, 10], 9: [1, 3, 4, 5, 6, 7], 10: [0, 1, 2, 3, 5, 6, 8]})
MPG_11_35 = Graph({0: [2, 4, 5, 6, 8, 9], 1: [3, 5, 6, 7, 8, 10], 2: [0, 4, 7, 8, 9, 10], 3: [1, 5, 6, 7, 9, 10], 4: [0, 2, 7, 8, 9, 10], 5: [0, 1, 3, 6, 8, 9], 6: [0, 1, 3, 5, 8, 10], 7: [1, 2, 3, 4, 9, 10], 8: [0, 1, 2, 4, 5, 6, 10], 9: [0, 2, 3, 4, 5, 7], 10: [1, 2, 3, 4, 6, 7, 8]})
MPG_11_36 = Graph({0: [2, 4, 5, 6, 8, 9, 10], 1: [3, 5, 6, 7, 8, 10], 2: [0, 4, 7, 8, 9, 10], 3: [1, 5, 6, 7, 9], 4: [0, 2, 7, 8, 9, 10], 5: [0, 1, 3, 6, 8, 10], 6: [0, 1, 3, 5, 9, 10], 7: [1, 2, 3, 4, 8, 9], 8: [0, 1, 2, 4, 5, 7, 10], 9: [0, 2, 3, 4, 6, 7], 10: [0, 1, 2, 4, 5, 6, 8]})
MPG_11_37 = Graph({0: [2, 4, 5, 6, 8, 9, 10], 1: [3, 5, 6, 7, 8, 10], 2: [0, 4, 7, 8, 9, 10], 3: [1, 5, 6, 7, 9], 4: [0, 2, 7, 8, 9, 10], 5: [0, 1, 3, 6, 8, 10], 6: [0, 1, 3, 5, 9], 7: [1, 2, 3, 4, 8, 9, 10], 8: [0, 1, 2, 4, 5, 7, 10], 9: [0, 2, 3, 4, 6, 7], 10: [0, 1, 2, 4, 5, 7, 8]})
MPG_11_38 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 7], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 8, 9, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 8, 9, 10], 6: [0, 2, 4, 7, 8, 9, 10], 7: [0, 1, 2, 4, 6], 8: [0, 2, 3, 4, 5, 6, 9, 10], 9: [0, 2, 3, 4, 5, 6, 8, 10], 10: [0, 2, 3, 4, 5, 6, 8, 9]})
MPG_11_39 = Graph({0: [2, 4, 5, 7, 8, 9], 1: [3, 5, 6, 7, 8, 9, 10], 2: [0, 4, 6, 7, 8, 10], 3: [1, 5, 6, 7, 8, 9, 10], 4: [0, 2, 6, 9, 10], 5: [0, 1, 3, 7, 8, 9], 6: [1, 2, 3, 4, 9, 10], 7: [0, 1, 2, 3, 5, 8, 10], 8: [0, 1, 2, 3, 5, 7, 10], 9: [0, 1, 3, 4, 5, 6], 10: [1, 2, 3, 4, 6, 7, 8]})
MPG_11_40 = Graph({0: [2, 4, 5, 7, 8, 9], 1: [3, 5, 6, 7, 8, 9, 10], 2: [0, 4, 6, 7, 8, 10], 3: [1, 5, 6, 7, 8, 9, 10], 4: [0, 2, 6, 9], 5: [0, 1, 3, 7, 8, 9, 10], 6: [1, 2, 3, 4, 9, 10], 7: [0, 1, 2, 3, 5, 8, 10], 8: [0, 1, 2, 3, 5, 7, 10], 9: [0, 1, 3, 4, 5, 6], 10: [1, 2, 3, 5, 6, 7, 8]})
MPG_11_41 = Graph({0: [2, 4, 5, 7, 8, 9, 10], 1: [3, 5, 6, 7, 9], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 6, 8, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [0, 1, 3, 8, 9], 6: [1, 2, 3, 4, 7, 8, 10], 7: [0, 1, 2, 4, 6, 9, 10], 8: [0, 2, 3, 4, 5, 6, 10], 9: [0, 1, 2, 4, 5, 7], 10: [0, 2, 3, 4, 6, 7, 8]})
MPG_11_42 = Graph({0: [2, 4, 5, 7, 8, 9, 10], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 6, 8], 4: [0, 2, 6, 7, 8, 9, 10], 5: [0, 1, 3, 8, 9], 6: [1, 2, 3, 4, 7, 8, 10], 7: [0, 1, 2, 4, 6, 9, 10], 8: [0, 2, 3, 4, 5, 6], 9: [0, 1, 2, 4, 5, 7, 10], 10: [0, 1, 2, 4, 6, 7, 9]})
MPG_11_43 = Graph({0: [2, 4, 5, 7, 8, 9], 1: [3, 5, 6, 7, 9, 10], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 6, 8, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [0, 1, 3, 8, 9], 6: [1, 2, 3, 4, 7, 8, 10], 7: [0, 1, 2, 4, 6, 9, 10], 8: [0, 2, 3, 4, 5, 6], 9: [0, 1, 2, 4, 5, 7, 10], 10: [1, 2, 3, 4, 6, 7, 9]})
MPG_11_44 = Graph({0: [2, 4, 5, 7, 8, 9, 10], 1: [3, 5, 6, 7, 9], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 6, 8], 4: [0, 2, 6, 7, 8, 9, 10], 5: [0, 1, 3, 8, 9], 6: [1, 2, 3, 4, 7, 8, 10], 7: [0, 1, 2, 4, 6, 9, 10], 8: [0, 2, 3, 4, 5, 6, 10], 9: [0, 1, 2, 4, 5, 7, 10], 10: [0, 2, 4, 6, 7, 8, 9]})
MPG_11_45 = Graph({0: [2, 4, 5, 8, 9], 1: [3, 5, 6, 7, 8, 9, 10], 2: [0, 4, 6, 7, 8, 10], 3: [1, 5, 6, 7, 8, 9, 10], 4: [0, 2, 6, 7, 9, 10], 5: [0, 1, 3, 8, 9], 6: [1, 2, 3, 4, 7, 8, 10], 7: [1, 2, 3, 4, 6, 9, 10], 8: [0, 1, 2, 3, 5, 6, 10], 9: [0, 1, 3, 4, 5, 7], 10: [1, 2, 3, 4, 6, 7, 8]})
MPG_11_46 = Graph({0: [2, 4, 5, 8, 9], 1: [3, 5, 6, 7, 8, 9, 10], 2: [0, 4, 6, 7, 8], 3: [1, 5, 6, 7, 8, 9, 10], 4: [0, 2, 6, 7, 9], 5: [0, 1, 3, 8, 9, 10], 6: [1, 2, 3, 4, 7, 8, 10], 7: [1, 2, 3, 4, 6, 9, 10], 8: [0, 1, 2, 3, 5, 6, 10], 9: [0, 1, 3, 4, 5, 7, 10], 10: [1, 3, 5, 6, 7, 8, 9]})
MPG_11_47 = Graph({0: [2, 4, 6, 7, 8, 9, 10], 1: [3, 5, 6], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 7, 8, 9, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [1, 3, 7, 8, 9, 10], 6: [0, 1, 2, 4], 7: [0, 2, 3, 4, 5, 8, 9, 10], 8: [0, 2, 3, 4, 5, 7, 9, 10], 9: [0, 2, 3, 4, 5, 7, 8, 10], 10: [0, 2, 3, 4, 5, 7, 8, 9]})
MPG_11_48 = Graph({0: [2, 4, 5, 6, 8, 9, 10], 1: [3, 4, 6, 7, 8, 10], 2: [0, 4, 5, 7, 9, 10], 3: [1, 5, 6, 7, 8, 9], 4: [0, 1, 2, 6, 7, 9, 10], 5: [0, 2, 3, 7, 8, 9, 10], 6: [0, 1, 3, 4, 8, 9], 7: [1, 2, 3, 4, 5, 9, 10], 8: [0, 1, 3, 5, 6, 10], 9: [0, 2, 3, 4, 5, 6, 7], 10: [0, 1, 2, 4, 5, 7, 8]})
MPG_11_49 = Graph({0: [2, 4, 5], 1: [3, 5, 6, 7, 8, 9, 10], 2: [0, 4, 6, 7, 8, 9, 10], 3: [1, 5, 6, 7, 8, 9, 10], 4: [0, 2, 6, 7, 8, 9, 10], 5: [0, 1, 3], 6: [1, 2, 3, 4, 7, 8, 9, 10], 7: [1, 2, 3, 4, 6, 8, 9, 10], 8: [1, 2, 3, 4, 6, 7, 9, 10], 9: [1, 2, 3, 4, 6, 7, 8, 10], 10: [1, 2, 3, 4, 6, 7, 8, 9]})
MPG_11_50 = Graph({0: [2, 3, 5, 6, 8, 9, 10], 1: [3, 4, 5, 6, 7, 8, 10], 2: [0, 4, 5, 7, 8, 9, 10], 3: [0, 1, 5, 6, 7, 9], 4: [1, 2, 6, 7, 8, 9, 10], 5: [0, 1, 2, 3, 7, 8, 10], 6: [0, 1, 3, 4, 8, 9, 10], 7: [1, 2, 3, 4, 5, 9], 8: [0, 1, 2, 4, 5, 6, 10], 9: [0, 2, 3, 4, 6, 7], 10: [0, 1, 2, 4, 5, 6, 8]})
MPG_11_51 = Graph({0: [2, 4, 5, 6, 7, 8, 9, 10], 1: [3, 8, 10], 2: [0, 4, 5, 6, 7, 8, 9, 10], 3: [1, 9], 4: [0, 2, 5, 6, 7, 8, 9, 10], 5: [0, 2, 4, 6, 7, 8, 9, 10], 6: [0, 2, 4, 5, 7, 8, 9, 10], 7: [0, 2, 4, 5, 6, 8, 9, 10], 8: [0, 1, 2, 4, 5, 6, 7, 10], 9: [0, 2, 3, 4, 5, 6, 7], 10: [0, 1, 2, 4, 5, 6, 7, 8]})
MPG_11_52 = Graph({0: [2, 4, 5, 6, 7, 8, 9, 10], 1: [3, 8], 2: [0, 4, 5, 6, 7, 8, 9, 10], 3: [1, 9], 4: [0, 2, 5, 6, 7, 8, 9, 10], 5: [0, 2, 4, 6, 7, 8, 9, 10], 6: [0, 2, 4, 5, 7, 8, 9, 10], 7: [0, 2, 4, 5, 6, 8, 9, 10], 8: [0, 1, 2, 4, 5, 6, 7, 10], 9: [0, 2, 3, 4, 5, 6, 7, 10], 10: [0, 2, 4, 5, 6, 7, 8, 9]})
MPG_11_53 = Graph({0: [2, 4, 5, 6, 7, 8, 9, 10], 1: [3, 7, 9, 10], 2: [0, 4, 5, 6, 7, 8, 9, 10], 3: [1, 8], 4: [0, 2, 5, 6, 7, 8, 9, 10], 5: [0, 2, 4, 6, 7, 8, 9, 10], 6: [0, 2, 4, 5, 7, 8, 9, 10], 7: [0, 1, 2, 4, 5, 6, 9, 10], 8: [0, 2, 3, 4, 5, 6], 9: [0, 1, 2, 4, 5, 6, 7, 10], 10: [0, 1, 2, 4, 5, 6, 7, 9]})
MPG_11_54 = Graph({0: [2, 4, 5, 6, 7, 8, 9, 10], 1: [3, 6, 8, 9, 10], 2: [0, 4, 5, 6, 7, 8, 9, 10], 3: [1, 7], 4: [0, 2, 5, 6, 7, 8, 9, 10], 5: [0, 2, 4, 6, 7, 8, 9, 10], 6: [0, 1, 2, 4, 5, 8, 9, 10], 7: [0, 2, 3, 4, 5], 8: [0, 1, 2, 4, 5, 6, 9, 10], 9: [0, 1, 2, 4, 5, 6, 8, 10], 10: [0, 1, 2, 4, 5, 6, 8, 9]})
MPG_11_0.name("MPG_11_0")
MPG_11_1.name("MPG_11_1")
MPG_11_2.name("MPG_11_2")
MPG_11_3.name("MPG_11_3")
MPG_11_4.name("MPG_11_4")
MPG_11_5.name("MPG_11_5")
MPG_11_6.name("MPG_11_6")
MPG_11_7.name("MPG_11_7")
MPG_11_8.name("MPG_11_8")
MPG_11_9.name("MPG_11_9")
MPG_11_10.name("MPG_11_10")
MPG_11_11.name("MPG_11_11")
MPG_11_12.name("MPG_11_12")
MPG_11_13.name("MPG_11_13")
MPG_11_14.name("MPG_11_14")
MPG_11_15.name("MPG_11_15")
MPG_11_16.name("MPG_11_16")
MPG_11_17.name("MPG_11_17")
MPG_11_18.name("MPG_11_18")
MPG_11_19.name("MPG_11_19")
MPG_11_20.name("MPG_11_20")
MPG_11_21.name("MPG_11_21")
MPG_11_22.name("MPG_11_22")
MPG_11_23.name("MPG_11_23")
MPG_11_24.name("MPG_11_24")
MPG_11_25.name("MPG_11_25")
MPG_11_26.name("MPG_11_26")
MPG_11_27.name("MPG_11_27")
MPG_11_28.name("MPG_11_28")
MPG_11_29.name("MPG_11_29")
MPG_11_30.name("MPG_11_30")
MPG_11_31.name("MPG_11_31")
MPG_11_32.name("MPG_11_32")
MPG_11_33.name("MPG_11_33")
MPG_11_34.name("MPG_11_34")
MPG_11_35.name("MPG_11_35")
MPG_11_36.name("MPG_11_36")
MPG_11_37.name("MPG_11_37")
MPG_11_38.name("MPG_11_38")
MPG_11_39.name("MPG_11_39")
MPG_11_40.name("MPG_11_40")
MPG_11_41.name("MPG_11_41")
MPG_11_42.name("MPG_11_42")
MPG_11_43.name("MPG_11_43")
MPG_11_44.name("MPG_11_44")
MPG_11_45.name("MPG_11_45")
MPG_11_46.name("MPG_11_46")
MPG_11_47.name("MPG_11_47")
MPG_11_48.name("MPG_11_48")
MPG_11_49.name("MPG_11_49")
MPG_11_50.name("MPG_11_50")
MPG_11_51.name("MPG_11_51")
MPG_11_52.name("MPG_11_52")
MPG_11_53.name("MPG_11_53")
MPG_11_54.name("MPG_11_54")

MPGS_11 = [MPG_11_0, MPG_11_1, MPG_11_2, MPG_11_3, MPG_11_4, MPG_11_5, MPG_11_6, MPG_11_7, MPG_11_8, MPG_11_9, MPG_11_10, MPG_11_11, MPG_11_12, MPG_11_13, MPG_11_14, MPG_11_15, MPG_11_16, MPG_11_17, MPG_11_18, MPG_11_19, MPG_11_20, MPG_11_21, MPG_11_22, MPG_11_23, MPG_11_24, MPG_11_25, MPG_11_26, MPG_11_27, MPG_11_28, MPG_11_29, MPG_11_30, MPG_11_31, MPG_11_32, MPG_11_33, MPG_11_34, MPG_11_35, MPG_11_36, MPG_11_37, MPG_11_38, MPG_11_39, MPG_11_40, MPG_11_41, MPG_11_42, MPG_11_43, MPG_11_44, MPG_11_45, MPG_11_46, MPG_11_47, MPG_11_48, MPG_11_49, MPG_11_50, MPG_11_51, MPG_11_52, MPG_11_53, MPG_11_54]


MPGS = MPGS_5 + MPGS_6 + MPGS_7 + MPGS_8 + MPGS_9 + MPGS_10 + MPGS_11

MPGS_L = [[], [], [], [], [], MPGS_5, MPGS_6, MPGS_7, MPGS_8, MPGS_9, MPGS_10, MPGS_11]