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On this page are computer-accessible forms for the graph C4[ 156, 15 ] = SDD(C_39(1,14)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {75, 79} under the group generated by the following permutations:

a: (21, 78)
b: (16, 26)
c: (6, 48)
d: (5, 49)
e: (36, 55)
f: (52, 61)
g: (11, 34)
h: (14, 31)
m: (38, 62)
n1: (10, 72)
a1: (17, 67)
b1: (45, 59)
c1: (30, 47)
d1: (24, 57)
e1: (28, 46)
f1: (22, 76)
g1: (2, 4)(5, 11)(6, 12)(7, 17)(10, 21)(13, 28)(14, 24)(15, 16)(18, 35)(22, 40)(25, 41)(26, 27)(29, 51)(30, 52)(31, 57)(32, 46)(33, 48)(34, 49)(36, 42)(47, 61)(54, 67)(55, 66)(56, 69)(58, 65)(71, 76)(72, 78)(79, 80)(81, 84)(82, 85)(83, 91)(86, 99)(87, 95)(88, 104)(89, 97)(90, 98)(92, 109)(93, 110)(94, 115)(96, 120)(100, 123)(101, 124)(102, 127)(103, 119)(105, 129)(106, 117)(107, 116)(108, 132)(111, 137)(112, 135)(113, 126)(114, 125)(118, 142)(121, 144)(122, 133)(128, 143)(130, 146)(131, 140)(134, 149)(136, 153)(138, 154)(139, 155)(141, 152)(145, 148)(147, 150)(151, 156)
h1: (12, 33)
m1: (4, 58)
n2: (13, 32)
a2: (35, 51)
b2: (9, 53)
c2: (8, 63)
d2: (23, 37)
e2: (3, 70)
f2: (42, 66)
g2: (19, 44)
h2: (18, 29)
m2: (60, 77)
n3: (2, 5)(3, 8)(4, 11)(6, 15)(7, 14)(9, 19)(10, 21)(12, 16)(13, 18)(17, 24)(20, 23)(22, 41)(25, 40)(26, 33)(27, 48)(28, 35)(29, 32)(30, 36)(31, 54)(34, 58)(37, 43)(38, 45)(39, 50)(42, 52)(44, 53)(46, 51)(47, 55)(49, 65)(56, 71)(57, 67)(59, 62)(60, 68)(61, 66)(63, 70)(64, 74)(69, 76)(72, 78)(73, 77)(79, 81)(80, 84)(82, 89)(83, 92)(85, 97)(86, 100)(87, 88)(90, 106)(91, 109)(93, 113)(94, 116)(95, 104)(96, 112)(98, 117)(99, 123)(101, 125)(103, 105)(107, 115)(108, 133)(110, 126)(111, 138)(114, 124)(118, 140)(119, 129)(120, 135)(121, 141)(122, 132)(128, 130)(131, 142)(134, 150)(136, 148)(137, 154)(139, 156)(143, 146)(144, 152)(145, 153)(147, 149)(151, 155)
a3: (50, 64)
b3: (1, 2)(3, 7)(4, 10)(5, 13)(6, 8)(9, 18)(11, 23)(12, 25)(15, 30)(16, 19)(17, 22)(20, 36)(21, 39)(24, 45)(26, 44)(27, 47)(28, 50)(29, 53)(32, 49)(33, 56)(34, 37)(35, 42)(38, 40)(41, 60)(43, 55)(46, 64)(48, 63)(51, 66)(52, 68)(54, 70)(57, 59)(58, 72)(61, 73)(62, 71)(65, 75)(67, 76)(69, 77)(74, 78)(80, 83)(81, 86)(82, 88)(84, 94)(85, 96)(87, 102)(89, 101)(90, 105)(91, 108)(92, 111)(93, 104)(95, 118)(97, 117)(98, 121)(99, 122)(100, 103)(106, 126)(107, 130)(109, 115)(110, 136)(112, 140)(113, 139)(114, 129)(116, 141)(119, 138)(120, 134)(123, 146)(124, 147)(125, 128)(127, 145)(131, 148)(133, 137)(135, 142)(143, 156)(144, 151)(149, 153)(150, 155)(152, 154)
c3: (20, 43)
d3: (68, 73)
e3: (39, 74)
f3: (25, 56)
g3: (41, 69)
h3: (2, 65)
m3: (15, 27)
n4: (40, 71)

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

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