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On this page are computer-accessible forms for the graph C4[ 144, 16 ] = R_72(20,55).

(I) Following is a form readable by MAGMA:

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

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

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