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On this page are computer-accessible forms for the graph C4[ 144, 15 ] = R_72(56,19).

(I) Following is a form readable by MAGMA:

g:=Graph<144|{ {2, 3}, {46, 47}, {44, 45}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32, 33}, {30, 31}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {48, 49}, {50, 51}, {52, 53}, {54, 55}, {56, 57}, {58, 59}, {60, 61}, {62, 63}, {64, 65}, {66, 67}, {68, 69}, {70, 71}, {1, 2}, {45, 46}, {41, 42}, {37, 38}, {33, 34}, {29, 30}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {49, 50}, {53, 54}, {57, 58}, {61, 62}, {65, 66}, {69, 70}, {3, 4}, {43, 44}, {35, 36}, {11, 12}, {19, 20}, {27, 28}, {51, 52}, {59, 60}, {67, 68}, {7, 8}, {39, 40}, {23, 24}, {55, 56}, {71, 72}, {64, 80}, {65, 81}, {66, 82}, {67, 83}, {68, 84}, {69, 85}, {70, 86}, {71, 87}, {72, 88}, {76, 95}, {108, 127}, {104, 123}, {96, 115}, {100, 119}, {73, 92}, {107, 126}, {105, 124}, {75, 94}, {97, 116}, {99, 118}, {74, 93}, {106, 125}, {98, 117}, {101, 120}, {103, 122}, {15, 16}, {47, 48}, {102, 121}, {77, 96}, {79, 98}, {93, 112}, {95, 114}, {78, 97}, {94, 113}, {80, 99}, {84, 103}, {88, 107}, {92, 111}, {74, 127}, {81, 100}, {83, 102}, {89, 108}, {91, 110}, {73, 126}, {82, 101}, {90, 109}, {85, 104}, {87, 106}, {31, 32}, {86, 105}, {1, 73}, {39, 111}, {38, 110}, {37, 109}, {36, 108}, {35, 107}, {34, 106}, {33, 105}, {32, 104}, {2, 74}, {3, 75}, {4, 76}, {5, 77}, {6, 78}, {7, 79}, {16, 88}, {17, 89}, {18, 90}, {19, 91}, {20, 92}, {21, 93}, {22, 94}, {23, 95}, {48, 120}, {49, 121}, {50, 122}, {51, 123}, {52, 124}, {53, 125}, {54, 126}, {55, 127}, {1, 72}, {1, 89}, {47, 119}, {46, 118}, {45, 117}, {44, 116}, {43, 115}, {42, 114}, {41, 113}, {40, 112}, {39, 127}, {38, 126}, {37, 125}, {36, 124}, {35, 123}, {34, 122}, {33, 121}, {32, 120}, {2, 90}, {3, 91}, {4, 92}, {5, 93}, {6, 94}, {7, 95}, {8, 80}, {9, 81}, {10, 82}, {11, 83}, {12, 84}, {13, 85}, {14, 86}, {15, 87}, {8, 96}, {31, 119}, {30, 118}, {29, 117}, {28, 116}, {9, 97}, {10, 98}, {11, 99}, {12, 100}, {13, 101}, {14, 102}, {15, 103}, {24, 112}, {25, 113}, {26, 114}, {27, 115}, {57, 73}, {58, 74}, {59, 75}, {60, 76}, {61, 77}, {62, 78}, {63, 79}, {16, 104}, {31, 103}, {30, 102}, {29, 101}, {17, 105}, {18, 106}, {19, 107}, {20, 108}, {21, 109}, {22, 110}, {23, 111}, {24, 96}, {25, 97}, {26, 98}, {27, 99}, {28, 100}, {63, 64}, {40, 128}, {47, 135}, {46, 134}, {45, 133}, {44, 132}, {43, 131}, {42, 130}, {41, 129}, {56, 144}, {48, 136}, {49, 137}, {50, 138}, {51, 139}, {52, 140}, {53, 141}, {54, 142}, {55, 143}, {56, 128}, {57, 129}, {58, 130}, {59, 131}, {60, 132}, {61, 133}, {62, 134}, {63, 135}, {64, 136}, {65, 137}, {66, 138}, {67, 139}, {68, 140}, {69, 141}, {70, 142}, {71, 143}, {75, 128}, {79, 132}, {91, 144}, {76, 129}, {78, 131}, {77, 130}, {80, 133}, {82, 135}, {88, 141}, {90, 143}, {81, 134}, {89, 142}, {72, 144}, {83, 136}, {87, 140}, {84, 137}, {86, 139}, {85, 138}, {109, 128}, {125, 144}, {111, 130}, {110, 129}, {112, 131}, {124, 143}, {120, 139}, {116, 135}, {113, 132}, {123, 142}, {121, 140}, {115, 134}, {114, 133}, {122, 141}, {117, 136}, {119, 138}, {118, 137} }>;

(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: (3, 74)(4, 58)(5, 59)(6, 131)(7, 43)(8, 44)(9, 116)(10, 28)(11, 29)(12, 101)(15, 86)(16, 70)(17, 71)(18, 143)(19, 55)(20, 56)(21, 128)(22, 40)(23, 41)(24, 113)(27, 98)(30, 83)(31, 67)(32, 68)(33, 140)(34, 52)(35, 53)(36, 125)(39, 110)(42, 95)(45, 80)(46, 64)(47, 65)(48, 137)(51, 122)(54, 107)(57, 92)(60, 77)(63, 134)(66, 119)(69, 104)(72, 89)(75, 93)(76, 130)(79, 115)(81, 135)(82, 100)(84, 120)(87, 105)(88, 142)(91, 127)(94, 112)(96, 132)(99, 117)(103, 139)(106, 124)(108, 144)(111, 129)(118, 136)(123, 141)
b: (2, 72, 73, 89)(3, 88, 92, 17)(4, 16)(5, 15, 76, 104)(6, 103, 95, 32)(7, 31)(8, 30, 79, 119)(9, 118, 98, 47)(10, 46)(11, 45, 82, 134)(12, 133, 101, 62)(13, 61)(14, 60, 85, 77)(18, 91, 107, 20)(21, 106, 110, 35)(22, 34)(23, 33, 94, 122)(24, 121, 113, 50)(25, 49)(26, 48, 97, 137)(27, 136, 116, 65)(28, 64)(29, 63, 100, 80)(36, 109, 125, 38)(39, 124, 128, 53)(40, 52)(41, 51, 112, 140)(42, 139, 131, 68)(43, 67)(44, 66, 115, 83)(54, 127, 143, 56)(57, 142, 74, 71)(58, 70)(59, 69, 130, 86)(75, 141, 111, 105)(78, 84, 114, 120)(81, 99, 117, 135)(87, 129, 123, 93)(90, 144, 126, 108)(96, 102, 132, 138)
c: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72)(73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144)

(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[ 144, 15 ]
144
-1 89 2 72 73
-2 1 90 3 74
-3 2 91 4 75
-4 3 92 5 76
-5 77 4 93 6
-6 78 5 94 7
-7 79 6 95 8
-8 80 7 96 9
-9 81 8 97 10
-10 11 82 9 98
-11 99 12 83 10
-12 11 100 13 84
-13 12 101 14 85
-14 13 102 15 86
-15 14 103 16 87
-16 88 15 104 17
-17 89 16 105 18
-18 90 17 106 19
-19 91 18 107 20
-20 92 19 108 21
-21 22 93 20 109
-22 110 23 94 21
-23 22 111 24 95
-24 23 112 25 96
-25 24 113 26 97
-26 25 114 27 98
-27 99 26 115 28
-28 100 27 116 29
-29 101 28 117 30
-30 102 29 118 31
-31 103 30 119 32
-32 33 104 31 120
-33 121 34 105 32
-34 33 122 35 106
-35 34 123 36 107
-36 35 124 37 108
-37 36 125 38 109
-38 110 37 126 39
-39 111 38 127 40
-40 112 39 128 41
-41 113 40 129 42
-42 114 41 130 43
-43 44 115 42 131
-44 132 45 116 43
-45 44 133 46 117
-46 45 134 47 118
-47 46 135 48 119
-48 47 136 49 120
-49 121 48 137 50
-50 122 49 138 51
-51 123 50 139 52
-52 124 51 140 53
-53 125 52 141 54
-54 55 126 53 142
-55 143 56 127 54
-56 55 144 57 128
-57 56 58 73 129
-58 57 59 74 130
-59 58 60 75 131
-60 132 59 61 76
-61 77 133 60 62
-62 78 134 61 63
-63 79 135 62 64
-64 80 136 63 65
-65 66 81 137 64
-66 67 82 138 65
-67 66 68 83 139
-68 67 69 84 140
-69 68 70 85 141
-70 69 71 86 142
-71 143 70 72 87
-72 88 1 144 71
-73 1 57 92 126
-74 2 58 93 127
-75 3 59 94 128
-76 4 60 95 129
-77 5 61 96 130
-78 6 62 97 131
-79 132 7 63 98
-80 99 133 8 64
-81 100 134 9 65
-82 66 101 135 10
-83 11 67 102 136
-84 12 68 103 137
-85 13 69 104 138
-86 14 70 105 139
-87 15 71 106 140
-88 16 72 107 141
-89 1 17 108 142
-90 143 2 18 109
-91 110 144 3 19
-92 111 4 73 20
-93 112 5 74 21
-94 22 113 6 75
-95 23 114 7 76
-96 77 24 115 8
-97 78 25 116 9
-98 79 26 117 10
-99 11 80 27 118
-100 12 81 28 119
-101 13 82 29 120
-102 121 14 83 30
-103 122 15 84 31
-104 123 16 85 32
-105 33 124 17 86
-106 34 125 18 87
-107 88 35 126 19
-108 89 36 127 20
-109 90 37 128 21
-110 22 91 38 129
-111 23 92 39 130
-112 24 93 40 131
-113 132 25 94 41
-114 133 26 95 42
-115 134 27 96 43
-116 44 135 28 97
-117 45 136 29 98
-118 99 46 137 30
-119 100 47 138 31
-120 101 48 139 32
-121 33 102 49 140
-122 34 103 50 141
-123 35 104 51 142
-124 143 36 105 52
-125 144 37 106 53
-126 38 73 107 54
-127 55 39 74 108
-128 56 40 75 109
-129 110 57 41 76
-130 77 111 58 42
-131 78 112 59 43
-132 44 79 113 60
-133 45 80 114 61
-134 46 81 115 62
-135 47 82 116 63
-136 48 83 117 64
-137 49 84 118 65
-138 66 50 85 119
-139 67 51 86 120
-140 121 68 52 87
-141 88 122 69 53
-142 89 123 70 54
-143 55 90 124 71
-144 56 91 125 72
0

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