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On this page are computer-accessible forms for the graph C4[ 84, 18 ] = L(F56C).

(I) Following is a form readable by MAGMA:

g:=Graph<84|{ {2, 3}, {82, 83}, {80, 81}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {62, 63}, {22, 23}, {4, 5}, {32, 33}, {34, 35}, {38, 39}, {46, 47}, {50, 51}, {52, 53}, {54, 55}, {60, 61}, {1, 3}, {69, 71}, {21, 23}, {49, 51}, {52, 54}, {1, 2}, {69, 70}, {65, 66}, {29, 30}, {25, 26}, {37, 38}, {49, 50}, {57, 58}, {1, 5}, {80, 84}, {17, 21}, {16, 20}, {3, 7}, {2, 6}, {1, 4}, {81, 84}, {24, 29}, {10, 12}, {82, 84}, {25, 31}, {11, 13}, {59, 61}, {59, 60}, {83, 84}, {67, 68}, {4, 12}, {7, 15}, {6, 14}, {5, 13}, {34, 43}, {2, 8}, {22, 28}, {16, 26}, {3, 9}, {33, 42}, {68, 79}, {35, 40}, {39, 44}, {66, 78}, {71, 75}, {67, 79}, {19, 30}, {4, 10}, {7, 9}, {6, 8}, {5, 11}, {54, 56}, {55, 56}, {65, 78}, {42, 58}, {36, 53}, {11, 24}, {12, 31}, {6, 18}, {7, 19}, {12, 25}, {41, 60}, {10, 28}, {13, 27}, {11, 29}, {38, 48}, {43, 61}, {47, 57}, {37, 50}, {39, 48}, {40, 63}, {8, 16}, {72, 80}, {9, 17}, {73, 80}, {33, 59}, {75, 81}, {34, 56}, {32, 59}, {74, 81}, {35, 56}, {8, 20}, {79, 83}, {15, 19}, {14, 18}, {10, 22}, {9, 21}, {78, 83}, {45, 51}, {76, 82}, {46, 48}, {47, 48}, {77, 82}, {14, 42}, {15, 43}, {31, 57}, {22, 62}, {25, 49}, {23, 62}, {26, 49}, {28, 55}, {13, 32}, {27, 54}, {15, 34}, {14, 33}, {27, 52}, {31, 47}, {30, 45}, {16, 36}, {17, 37}, {18, 39}, {24, 46}, {17, 38}, {20, 35}, {27, 32}, {20, 40}, {21, 41}, {18, 44}, {26, 36}, {23, 41}, {19, 45}, {29, 69}, {24, 65}, {30, 69}, {28, 67}, {40, 73}, {43, 74}, {36, 70}, {44, 75}, {45, 68}, {42, 64}, {41, 66}, {44, 71}, {37, 72}, {46, 65}, {53, 70}, {55, 67}, {57, 77}, {63, 73}, {51, 68}, {58, 77}, {61, 74}, {52, 76}, {53, 76}, {50, 72}, {58, 64}, {60, 66}, {62, 64}, {63, 64} }>;

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

a: (1, 2, 3)(4, 6, 7)(5, 8, 9)(10, 14, 15)(11, 16, 17)(12, 18, 19)(13, 20, 21)(22, 33, 34)(23, 32, 35)(24, 36, 37)(25, 39, 30)(26, 38, 29)(27, 40, 41)(28, 42, 43)(31, 44, 45)(46, 70, 50)(47, 71, 51)(48, 69, 49)(52, 73, 66)(53, 72, 65)(54, 63, 60)(55, 64, 61)(56, 62, 59)(57, 75, 68)(58, 74, 67)(76, 80, 78)(77, 81, 79)(82, 84, 83)
b: (2, 4)(3, 5)(6, 10)(7, 11)(8, 12)(9, 13)(14, 22)(15, 24)(16, 25)(17, 27)(18, 28)(19, 29)(20, 31)(21, 32)(23, 33)(34, 46)(35, 47)(36, 49)(37, 52)(38, 54)(39, 55)(40, 57)(41, 59)(42, 62)(43, 65)(44, 67)(45, 69)(48, 56)(50, 53)(51, 70)(58, 63)(61, 66)(68, 71)(72, 76)(73, 77)(74, 78)(75, 79)(80, 82)(81, 83)
c: (2, 5, 3, 4)(6, 11, 9, 12)(7, 10, 8, 13)(14, 29, 21, 25)(15, 28, 20, 27)(16, 32, 19, 22)(17, 31, 18, 24)(23, 26, 33, 30)(34, 55, 35, 54)(36, 59, 45, 62)(37, 57, 44, 65)(38, 47, 39, 46)(40, 52, 43, 67)(41, 49, 42, 69)(50, 58, 71, 66)(51, 64, 70, 60)(53, 61, 68, 63)(72, 77, 75, 78)(73, 76, 74, 79)(80, 82, 81, 83)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

**************

&Graph
C4[ 84, 18 ]
84
-1 2 3 4 5
-2 1 3 6 8
-3 1 2 7 9
-4 1 12 5 10
-5 11 1 13 4
-6 2 14 18 8
-7 3 15 19 9
-8 2 16 6 20
-9 3 17 7 21
-10 22 12 4 28
-11 13 24 5 29
-12 25 4 31 10
-13 11 5 27 32
-14 33 6 18 42
-15 34 7 19 43
-16 36 26 8 20
-17 37 38 9 21
-18 44 14 6 39
-19 45 15 7 30
-20 35 16 40 8
-21 23 17 41 9
-22 23 28 62 10
-23 22 62 41 21
-24 11 46 29 65
-25 12 26 49 31
-26 25 36 16 49
-27 13 52 32 54
-28 22 55 67 10
-29 11 24 69 30
-30 45 69 29 19
-31 12 57 25 47
-32 33 13 59 27
-33 14 59 42 32
-34 56 35 15 43
-35 34 56 40 20
-36 26 70 16 53
-37 38 17 50 72
-38 37 48 17 39
-39 44 48 38 18
-40 35 73 63 20
-41 66 23 60 21
-42 33 14 58 64
-43 34 15 61 74
-44 71 39 18 75
-45 68 51 19 30
-46 24 47 48 65
-47 46 57 48 31
-48 46 47 38 39
-49 25 26 50 51
-50 37 49 72 51
-51 45 68 49 50
-52 27 53 54 76
-53 36 70 52 76
-54 55 56 27 52
-55 56 67 28 54
-56 55 34 35 54
-57 77 47 58 31
-58 77 57 42 64
-59 33 60 61 32
-60 66 59 61 41
-61 59 60 74 43
-62 22 23 63 64
-63 40 62 73 64
-64 58 62 63 42
-65 66 78 24 46
-66 78 60 41 65
-67 55 68 79 28
-68 45 67 79 51
-69 70 71 29 30
-70 36 69 71 53
-71 44 69 70 75
-72 80 37 50 73
-73 80 72 40 63
-74 81 61 75 43
-75 44 81 71 74
-76 77 82 52 53
-77 57 58 82 76
-78 66 79 83 65
-79 67 78 68 83
-80 81 72 73 84
-81 80 84 74 75
-82 77 83 84 76
-83 78 79 82 84
-84 80 81 82 83
0

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