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On this page are computer-accessible forms for the graph C4[ 152, 4 ] = R_76(40,39).

(I) Following is a form readable by MAGMA:

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

(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: (31, 106)(32, 145)(69, 144)(70, 107)
b: (4, 79)(5, 43)(6, 119)(42, 117)(44, 81)(80, 118)
c: (23, 98)(24, 137)(61, 136)(62, 99)
d: (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)
e: (8, 83)(9, 47)(10, 123)(46, 121)(48, 85)(84, 122)
f: (5, 80)(6, 119)(43, 118)(44, 81)
g: (17, 92)(18, 131)(55, 130)(56, 93)
h: (34, 109)(35, 73)(36, 149)(72, 147)(74, 111)(110, 148)
m: (24, 99)(25, 63)(26, 139)(62, 137)(64, 101)(100, 138)
n1: (2, 113)(3, 37)(4, 36)(5, 35)(6, 34)(7, 33)(8, 32)(9, 31)(10, 30)(11, 29)(12, 28)(13, 27)(14, 26)(15, 25)(16, 24)(17, 23)(18, 22)(19, 21)(38, 115)(40, 151)(41, 75)(42, 74)(43, 73)(44, 72)(45, 71)(46, 70)(47, 69)(48, 68)(49, 67)(50, 66)(51, 65)(52, 64)(53, 63)(54, 62)(55, 61)(56, 60)(57, 59)(76, 77)(78, 150)(79, 149)(80, 148)(81, 147)(82, 146)(83, 145)(84, 144)(85, 143)(86, 142)(87, 141)(88, 140)(89, 139)(90, 138)(91, 137)(92, 136)(93, 135)(94, 134)(95, 133)(96, 132)(97, 131)(98, 130)(99, 129)(100, 128)(101, 127)(102, 126)(103, 125)(104, 124)(105, 123)(106, 122)(107, 121)(108, 120)(109, 119)(110, 118)(111, 117)(112, 116)(114, 152)
a1: (22, 97)(23, 61)(24, 137)(60, 135)(62, 99)(98, 136)
b1: (37, 112)(38, 151)(75, 150)(76, 113)
c1: (16, 91)(17, 55)(18, 131)(54, 129)(56, 93)(92, 130)
d1: (10, 85)(11, 49)(12, 125)(48, 123)(50, 87)(86, 124)
e1: (27, 102)(28, 141)(65, 140)(66, 103)
f1: (26, 101)(27, 65)(28, 141)(64, 139)(66, 103)(102, 140)
g1: (6, 81)(7, 45)(8, 121)(44, 119)(46, 83)(82, 120)
h1: (18, 93)(19, 57)(20, 133)(56, 131)(58, 95)(94, 132)
m1: (19, 94)(20, 133)(57, 132)(58, 95)
n2: (20, 95)(21, 59)(22, 135)(58, 133)(60, 97)(96, 134)
a2: (25, 100)(26, 139)(63, 138)(64, 101)
b2: (14, 89)(15, 53)(16, 129)(52, 127)(54, 91)(90, 128)
c2: (36, 111)(37, 75)(38, 151)(74, 149)(76, 113)(112, 150)
d2: (35, 110)(36, 149)(73, 148)(74, 111)
e2: (32, 107)(33, 71)(34, 147)(70, 145)(72, 109)(108, 146)
f2: (12, 87)(13, 51)(14, 127)(50, 125)(52, 89)(88, 126)
g2: (9, 84)(10, 123)(47, 122)(48, 85)
h2: (28, 103)(29, 67)(30, 143)(66, 141)(68, 105)(104, 142)
m2: (7, 82)(8, 121)(45, 120)(46, 83)
n3: (21, 96)(22, 135)(59, 134)(60, 97)
a3: (13, 88)(14, 127)(51, 126)(52, 89)
b3: (11, 86)(12, 125)(49, 124)(50, 87)
c3: (29, 104)(30, 143)(67, 142)(68, 105)
d3: (30, 105)(31, 69)(32, 145)(68, 143)(70, 107)(106, 144)
e3: (33, 108)(34, 147)(71, 146)(72, 109)
f3: (15, 90)(16, 129)(53, 128)(54, 91)

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

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