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On this page are computer-accessible forms for the graph C4[ 96, 8 ] = PS(12,16;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 18} under the group generated by the following permutations:

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

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

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