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On this page are computer-accessible forms for the graph C4[ 96, 53 ] = SS[96,13].

(I) Following is a form readable by MAGMA:

g:=Graph<96|{ {1, 3}, {1, 2}, {84, 87}, {1, 5}, {81, 85}, {17, 21}, {1, 4}, {83, 86}, {82, 87}, {19, 22}, {51, 54}, {18, 20}, {16, 23}, {82, 85}, {81, 86}, {48, 55}, {50, 53}, {6, 14}, {6, 15}, {52, 61}, {51, 58}, {19, 26}, {17, 24}, {48, 57}, {6, 12}, {52, 62}, {7, 13}, {49, 59}, {50, 56}, {16, 27}, {83, 88}, {52, 63}, {18, 25}, {7, 11}, {84, 88}, {51, 63}, {7, 10}, {49, 60}, {6, 8}, {7, 9}, {48, 62}, {50, 61}, {11, 27}, {13, 29}, {42, 58}, {14, 31}, {78, 95}, {68, 85}, {36, 53}, {38, 55}, {40, 57}, {42, 59}, {43, 58}, {10, 24}, {76, 94}, {36, 54}, {15, 29}, {12, 30}, {37, 55}, {39, 53}, {43, 56}, {77, 94}, {72, 91}, {8, 28}, {75, 95}, {73, 93}, {40, 60}, {9, 28}, {67, 86}, {66, 87}, {11, 30}, {10, 31}, {41, 60}, {12, 26}, {14, 25}, {74, 93}, {13, 21}, {15, 22}, {65, 88}, {71, 92}, {8, 20}, {70, 90}, {69, 89}, {35, 63}, {32, 61}, {37, 56}, {38, 59}, {9, 23}, {39, 57}, {33, 62}, {64, 95}, {41, 54}, {10, 41}, {14, 43}, {13, 42}, {15, 40}, {12, 38}, {8, 36}, {11, 39}, {9, 37}, {79, 96}, {16, 32}, {80, 96}, {16, 33}, {19, 34}, {18, 35}, {17, 35}, {19, 33}, {18, 32}, {17, 34}, {21, 84}, {22, 83}, {20, 82}, {23, 81}, {26, 82}, {24, 81}, {25, 83}, {26, 80}, {27, 84}, {5, 86}, {3, 87}, {27, 79}, {25, 77}, {24, 76}, {2, 85}, {31, 72}, {29, 69}, {30, 70}, {3, 90}, {29, 68}, {20, 78}, {4, 95}, {28, 71}, {4, 88}, {23, 75}, {22, 74}, {21, 73}, {3, 94}, {31, 66}, {30, 67}, {28, 65}, {4, 89}, {2, 92}, {5, 91}, {2, 93}, {63, 96}, {44, 76}, {62, 94}, {61, 93}, {57, 89}, {45, 77}, {59, 90}, {34, 64}, {40, 75}, {58, 89}, {56, 91}, {44, 79}, {45, 78}, {42, 78}, {43, 79}, {5, 96}, {35, 70}, {34, 71}, {32, 69}, {44, 73}, {46, 72}, {44, 75}, {60, 91}, {45, 74}, {46, 70}, {33, 72}, {46, 71}, {38, 76}, {54, 92}, {39, 77}, {46, 69}, {55, 92}, {47, 68}, {47, 67}, {36, 73}, {47, 66}, {47, 65}, {37, 74}, {53, 90}, {49, 64}, {51, 66}, {48, 67}, {50, 65}, {52, 64}, {49, 68}, {41, 80}, {45, 80} }>;

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

a: (2, 5, 4, 3)(6, 7)(8, 10, 15, 11)(9, 14, 13, 12)(16, 18, 17, 19)(20, 24, 22, 27)(21, 26, 23, 25)(28, 31, 29, 30)(32, 35, 34, 33)(36, 41, 40, 39)(37, 43, 42, 38)(44, 45)(48, 50, 51, 49)(53, 54, 60, 57)(55, 56, 58, 59)(61, 63, 64, 62)(65, 66, 68, 67)(69, 70, 71, 72)(73, 80, 75, 77)(74, 79, 78, 76)(81, 83, 84, 82)(85, 86, 88, 87)(89, 90, 92, 91)(93, 96, 95, 94)
b: (3, 5)(6, 7)(8, 9)(10, 12)(11, 14)(13, 15)(16, 18)(17, 19)(20, 23)(21, 22)(24, 26)(25, 27)(30, 31)(33, 35)(36, 37)(38, 41)(39, 43)(40, 42)(44, 45)(48, 51)(53, 56)(54, 55)(57, 58)(59, 60)(62, 63)(66, 67)(70, 72)(73, 74)(75, 78)(76, 80)(77, 79)(81, 82)(83, 84)(86, 87)(90, 91)(94, 96)
c: (1, 20, 96, 36)(2, 82, 80, 54)(3, 78, 63, 73)(4, 18, 79, 53)(5, 8)(6, 91, 28, 86)(7, 48, 29, 33)(9, 67, 15, 72)(10, 55, 68, 19)(11, 57, 69, 16)(12, 60, 71, 81)(13, 62)(14, 56, 65, 83)(17, 76, 59, 64)(21, 94, 42, 52)(22, 31, 37, 47)(23, 30, 40, 46)(24, 38, 49, 34)(25, 43, 50, 88)(26, 41, 92, 85)(27, 39, 89, 32)(35, 44, 90, 95)(45, 51, 93, 87)(58, 61, 84, 77)(66, 74)(70, 75)
d: (1, 6)(2, 8)(3, 12)(4, 15)(5, 14)(7, 52)(9, 61)(10, 63)(11, 62)(13, 64)(18, 81)(19, 84)(20, 85)(21, 34)(22, 88)(23, 32)(24, 35)(25, 86)(26, 87)(27, 33)(28, 93)(29, 95)(30, 94)(31, 96)(36, 92)(37, 50)(38, 90)(39, 48)(40, 89)(41, 51)(42, 49)(43, 91)(44, 46)(45, 47)(53, 55)(58, 60)(65, 74)(66, 80)(67, 77)(68, 78)(69, 75)(70, 76)(71, 73)(72, 79)

(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.

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&Graph
C4[ 96, 53 ]
96
-1 2 3 4 5
-2 1 92 93 85
-3 1 90 94 87
-4 88 1 89 95
-5 1 91 96 86
-6 12 14 15 8
-7 11 13 9 10
-8 36 6 28 20
-9 23 37 28 7
-10 24 7 41 31
-11 27 39 7 30
-12 26 38 6 30
-13 7 29 42 21
-14 25 6 31 43
-15 22 6 29 40
-16 33 23 27 32
-17 34 24 35 21
-18 35 25 20 32
-19 22 33 34 26
-20 78 82 18 8
-21 13 17 73 84
-22 15 83 19 74
-23 81 16 9 75
-24 81 17 10 76
-25 77 14 83 18
-26 12 80 82 19
-27 11 79 16 84
-28 71 8 9 65
-29 13 68 69 15
-30 11 12 67 70
-31 66 14 72 10
-32 69 16 61 18
-33 16 72 62 19
-34 71 17 19 64
-35 70 17 18 63
-36 73 8 53 54
-37 55 56 74 9
-38 55 12 59 76
-39 11 77 57 53
-40 57 15 60 75
-41 80 60 10 54
-42 78 13 58 59
-43 56 79 14 58
-44 79 73 75 76
-45 77 78 80 74
-46 69 70 71 72
-47 66 67 68 65
-48 55 67 57 62
-49 68 59 60 64
-50 56 61 53 65
-51 66 58 63 54
-52 61 62 63 64
-53 90 36 39 50
-54 36 92 51 41
-55 37 48 92 38
-56 91 37 50 43
-57 89 48 39 40
-58 89 51 42 43
-59 90 38 49 42
-60 91 49 40 41
-61 93 50 52 32
-62 33 48 94 52
-63 35 51 52 96
-64 34 49 95 52
-65 88 47 28 50
-66 47 51 31 87
-67 47 48 30 86
-68 47 49 29 85
-69 89 46 29 32
-70 35 46 90 30
-71 34 46 92 28
-72 33 46 91 31
-73 44 36 93 21
-74 22 45 37 93
-75 44 23 40 95
-76 44 24 38 94
-77 45 25 39 94
-78 45 95 20 42
-79 44 27 96 43
-80 45 26 41 96
-81 23 24 85 86
-82 26 85 20 87
-83 22 88 25 86
-84 88 27 21 87
-85 2 68 81 82
-86 67 81 5 83
-87 66 3 82 84
-88 4 83 84 65
-89 57 58 69 4
-90 3 59 70 53
-91 56 5 60 72
-92 55 2 71 54
-93 2 61 73 74
-94 77 3 62 76
-95 78 4 64 75
-96 79 80 5 63
0

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