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On this page are computer-accessible forms for the graph C4[ 156, 11 ] = R_78(41,40).

(I) Following is a form readable by MAGMA:

g:=Graph<156|{ {2, 3}, {56, 57}, {54, 55}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {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}, {58, 59}, {60, 61}, {62, 63}, {64, 65}, {66, 67}, {68, 69}, {70, 71}, {72, 73}, {74, 75}, {76, 77}, {1, 2}, {57, 58}, {53, 54}, {49, 50}, {45, 46}, {41, 42}, {37, 38}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {61, 62}, {65, 66}, {69, 70}, {73, 74}, {77, 78}, {3, 4}, {51, 52}, {43, 44}, {35, 36}, {11, 12}, {19, 20}, {27, 28}, {59, 60}, {67, 68}, {75, 76}, {7, 8}, {55, 56}, {39, 40}, {23, 24}, {71, 72}, {15, 16}, {47, 48}, {64, 101}, {66, 103}, {72, 109}, {74, 111}, {80, 118}, {81, 119}, {88, 126}, {89, 127}, {65, 102}, {73, 110}, {80, 120}, {81, 121}, {82, 122}, {83, 123}, {84, 124}, {85, 125}, {86, 126}, {87, 127}, {82, 120}, {83, 121}, {86, 124}, {87, 125}, {67, 104}, {71, 108}, {68, 105}, {70, 107}, {84, 122}, {85, 123}, {69, 106}, {79, 119}, {79, 117}, {75, 112}, {76, 113}, {78, 115}, {31, 32}, {77, 114}, {1, 79}, {49, 127}, {48, 126}, {16, 94}, {17, 95}, {32, 110}, {33, 111}, {1, 78}, {2, 80}, {47, 125}, {46, 124}, {43, 121}, {42, 120}, {39, 117}, {38, 116}, {35, 113}, {3, 81}, {6, 84}, {7, 85}, {10, 88}, {11, 89}, {14, 92}, {15, 93}, {34, 112}, {4, 82}, {45, 123}, {44, 122}, {37, 115}, {36, 114}, {5, 83}, {12, 90}, {13, 91}, {59, 96}, {63, 100}, {60, 97}, {62, 99}, {8, 86}, {41, 119}, {40, 118}, {9, 87}, {61, 98}, {42, 79}, {56, 93}, {50, 87}, {48, 85}, {58, 95}, {49, 86}, {57, 94}, {51, 88}, {55, 92}, {52, 89}, {54, 91}, {53, 90}, {18, 96}, {19, 97}, {22, 100}, {23, 101}, {26, 104}, {27, 105}, {30, 108}, {31, 109}, {4, 119}, {8, 123}, {12, 127}, {1, 116}, {3, 118}, {9, 124}, {11, 126}, {20, 98}, {21, 99}, {28, 106}, {29, 107}, {2, 117}, {10, 125}, {43, 80}, {47, 84}, {5, 120}, {46, 83}, {44, 81}, {7, 122}, {24, 102}, {25, 103}, {6, 121}, {45, 82}, {63, 64}, {13, 128}, {15, 130}, {29, 144}, {31, 146}, {14, 129}, {30, 145}, {16, 131}, {20, 135}, {24, 139}, {28, 143}, {17, 132}, {19, 134}, {25, 140}, {27, 142}, {18, 133}, {26, 141}, {21, 136}, {23, 138}, {22, 137}, {50, 128}, {55, 133}, {54, 132}, {51, 129}, {58, 136}, {59, 137}, {62, 140}, {63, 141}, {32, 147}, {40, 155}, {36, 151}, {33, 148}, {41, 156}, {35, 150}, {52, 130}, {53, 131}, {60, 138}, {61, 139}, {34, 149}, {37, 152}, {39, 154}, {56, 134}, {57, 135}, {38, 153}, {64, 142}, {65, 143}, {66, 144}, {67, 145}, {70, 148}, {71, 149}, {74, 152}, {75, 153}, {78, 156}, {68, 146}, {69, 147}, {76, 154}, {77, 155}, {88, 128}, {89, 129}, {90, 130}, {91, 131}, {92, 132}, {93, 133}, {94, 134}, {95, 135}, {90, 128}, {91, 129}, {94, 132}, {95, 133}, {72, 150}, {73, 151}, {92, 130}, {93, 131}, {96, 134}, {113, 151}, {112, 150}, {97, 135}, {104, 142}, {105, 143}, {96, 136}, {116, 156}, {115, 155}, {114, 154}, {113, 153}, {112, 152}, {97, 137}, {98, 138}, {99, 139}, {100, 140}, {101, 141}, {102, 142}, {103, 143}, {98, 136}, {118, 156}, {115, 153}, {114, 152}, {99, 137}, {102, 140}, {103, 141}, {100, 138}, {117, 155}, {116, 154}, {101, 139}, {104, 144}, {111, 151}, {105, 145}, {106, 146}, {107, 147}, {108, 148}, {109, 149}, {110, 150}, {106, 144}, {107, 145}, {110, 148}, {111, 149}, {108, 146}, {109, 147} }>;

(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: (27, 104)(28, 144)(66, 143)(67, 105)
b: (11, 88)(12, 128)(50, 127)(51, 89)
c: (17, 94)(18, 134)(56, 133)(57, 95)
d: (29, 106)(30, 146)(68, 145)(69, 107)
e: (8, 85)(9, 48)(10, 126)(47, 124)(49, 87)(86, 125)
f: (22, 99)(23, 62)(24, 140)(61, 138)(63, 101)(100, 139)
g: (38, 115)(39, 155)(77, 154)(78, 116)
h: (13, 90)(14, 130)(52, 129)(53, 91)
m: (2, 116, 79, 78)(3, 38, 119, 115)(4, 37)(5, 36)(6, 35)(7, 34)(8, 33)(9, 32)(10, 31)(11, 30)(12, 29)(13, 28)(14, 27)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(39, 41, 155, 118)(42, 77, 80, 154)(43, 76)(44, 75)(45, 74)(46, 73)(47, 72)(48, 71)(49, 70)(50, 69)(51, 68)(52, 67)(53, 66)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)(81, 153)(82, 152)(83, 151)(84, 150)(85, 149)(86, 148)(87, 147)(88, 146)(89, 145)(90, 144)(91, 143)(92, 142)(93, 141)(94, 140)(95, 139)(96, 138)(97, 137)(98, 136)(99, 135)(100, 134)(101, 133)(102, 132)(103, 131)(104, 130)(105, 129)(106, 128)(107, 127)(108, 126)(109, 125)(110, 124)(111, 123)(112, 122)(113, 121)(114, 120)(117, 156)
n1: (20, 97)(21, 60)(22, 138)(59, 136)(61, 99)(98, 137)
a1: (14, 91)(15, 54)(16, 132)(53, 130)(55, 93)(92, 131)
b1: (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, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156)
c1: (7, 84)(8, 124)(46, 123)(47, 85)
d1: (34, 111)(35, 74)(36, 152)(73, 150)(75, 113)(112, 151)
e1: (16, 93)(17, 56)(18, 134)(55, 132)(57, 95)(94, 133)
f1: (9, 86)(10, 126)(48, 125)(49, 87)
g1: (23, 100)(24, 140)(62, 139)(63, 101)
h1: (21, 98)(22, 138)(60, 137)(61, 99)
m1: (19, 96)(20, 136)(58, 135)(59, 97)
n2: (10, 87)(11, 50)(12, 128)(49, 126)(51, 89)(88, 127)
a2: (12, 89)(13, 52)(14, 130)(51, 128)(53, 91)(90, 129)
b2: (5, 82)(6, 122)(44, 121)(45, 83)
c2: (35, 112)(36, 152)(74, 151)(75, 113)
d2: (15, 92)(16, 132)(54, 131)(55, 93)
e2: (26, 103)(27, 66)(28, 144)(65, 142)(67, 105)(104, 143)
f2: (36, 113)(37, 76)(38, 154)(75, 152)(77, 115)(114, 153)
g2: (32, 109)(33, 72)(34, 150)(71, 148)(73, 111)(110, 149)
h2: (25, 102)(26, 142)(64, 141)(65, 103)
m2: (18, 95)(19, 58)(20, 136)(57, 134)(59, 97)(96, 135)
n3: (24, 101)(25, 64)(26, 142)(63, 140)(65, 103)(102, 141)
a3: (31, 108)(32, 148)(70, 147)(71, 109)
b3: (6, 83)(7, 46)(8, 124)(45, 122)(47, 85)(84, 123)
c3: (4, 81)(5, 44)(6, 122)(43, 120)(45, 83)(82, 121)
d3: (30, 107)(31, 70)(32, 148)(69, 146)(71, 109)(108, 147)
e3: (37, 114)(38, 154)(76, 153)(77, 115)
f3: (33, 110)(34, 150)(72, 149)(73, 111)
g3: (28, 105)(29, 68)(30, 146)(67, 144)(69, 107)(106, 145)

(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[ 156, 11 ]
156
-1 78 2 79 116
-2 1 3 80 117
-3 2 4 81 118
-4 3 5 82 119
-5 4 6 83 120
-6 121 5 7 84
-7 122 6 8 85
-8 123 7 9 86
-9 124 8 10 87
-10 11 88 125 9
-11 12 89 126 10
-12 11 13 90 127
-13 12 14 91 128
-14 13 15 92 129
-15 14 16 93 130
-16 15 17 94 131
-17 132 16 18 95
-18 133 17 19 96
-19 134 18 20 97
-20 135 19 21 98
-21 22 99 136 20
-22 23 100 137 21
-23 22 24 101 138
-24 23 25 102 139
-25 24 26 103 140
-26 25 27 104 141
-27 26 28 105 142
-28 143 27 29 106
-29 144 28 30 107
-30 145 29 31 108
-31 146 30 32 109
-32 33 110 147 31
-33 34 111 148 32
-34 33 35 112 149
-35 34 36 113 150
-36 35 37 114 151
-37 36 38 115 152
-38 37 39 116 153
-39 154 38 40 117
-40 155 39 41 118
-41 156 40 42 119
-42 79 41 43 120
-43 44 121 80 42
-44 45 122 81 43
-45 44 46 123 82
-46 45 47 124 83
-47 46 48 125 84
-48 47 49 126 85
-49 48 50 127 86
-50 49 51 128 87
-51 88 50 52 129
-52 89 51 53 130
-53 90 52 54 131
-54 55 132 91 53
-55 56 133 92 54
-56 55 57 134 93
-57 56 58 135 94
-58 57 59 136 95
-59 58 60 137 96
-60 59 61 138 97
-61 60 62 139 98
-62 99 61 63 140
-63 100 62 64 141
-64 101 63 65 142
-65 66 143 102 64
-66 67 144 103 65
-67 66 68 145 104
-68 67 69 146 105
-69 68 70 147 106
-70 69 71 148 107
-71 70 72 149 108
-72 71 73 150 109
-73 110 72 74 151
-74 111 73 75 152
-75 112 74 76 153
-76 77 154 113 75
-77 78 155 114 76
-78 77 1 156 115
-79 1 117 42 119
-80 2 118 43 120
-81 44 121 3 119
-82 45 122 4 120
-83 121 46 123 5
-84 122 47 124 6
-85 123 48 125 7
-86 124 49 126 8
-87 125 50 127 9
-88 126 51 128 10
-89 11 127 52 129
-90 12 128 53 130
-91 13 129 54 131
-92 55 132 14 130
-93 56 133 15 131
-94 132 57 134 16
-95 133 58 135 17
-96 134 59 136 18
-97 135 60 137 19
-98 136 61 138 20
-99 137 62 139 21
-100 22 138 63 140
-101 23 139 64 141
-102 24 140 65 142
-103 66 143 25 141
-104 67 144 26 142
-105 143 68 145 27
-106 144 69 146 28
-107 145 70 147 29
-108 146 71 148 30
-109 147 72 149 31
-110 148 73 150 32
-111 33 149 74 151
-112 34 150 75 152
-113 35 151 76 153
-114 77 154 36 152
-115 78 155 37 153
-116 154 1 156 38
-117 155 2 79 39
-118 156 3 80 40
-119 79 4 81 41
-120 80 5 82 42
-121 81 6 83 43
-122 44 82 7 84
-123 45 83 8 85
-124 46 84 9 86
-125 47 85 10 87
-126 11 88 48 86
-127 12 89 49 87
-128 88 13 90 50
-129 89 14 91 51
-130 90 15 92 52
-131 91 16 93 53
-132 92 17 94 54
-133 55 93 18 95
-134 56 94 19 96
-135 57 95 20 97
-136 58 96 21 98
-137 22 99 59 97
-138 23 100 60 98
-139 99 24 101 61
-140 100 25 102 62
-141 101 26 103 63
-142 102 27 104 64
-143 103 28 105 65
-144 66 104 29 106
-145 67 105 30 107
-146 68 106 31 108
-147 69 107 32 109
-148 33 110 70 108
-149 34 111 71 109
-150 110 35 112 72
-151 111 36 113 73
-152 112 37 114 74
-153 113 38 115 75
-154 114 39 116 76
-155 77 115 40 117
-156 78 116 41 118
0

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