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On this page are computer-accessible forms for the graph C4[ 168, 60 ] = SDD(MC3(6,7,1,3,3,0,1)).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {72, 107}, {84, 119}, {80, 115}, {76, 111}, {73, 108}, {83, 118}, {81, 116}, {75, 110}, {64, 103}, {82, 117}, {74, 109}, {65, 104}, {66, 104}, {84, 126}, {81, 123}, {80, 122}, {67, 104}, {69, 105}, {68, 105}, {71, 106}, {65, 111}, {83, 125}, {82, 124}, {70, 105}, {68, 112}, {71, 113}, {79, 121}, {78, 120}, {66, 120}, {77, 119}, {76, 118}, {73, 115}, {72, 114}, {70, 125}, {69, 121}, {77, 112}, {79, 114}, {64, 126}, {75, 117}, {74, 116}, {67, 124}, {78, 113}, {27, 91}, {61, 125}, {38, 102}, {57, 121}, {26, 91}, {29, 92}, {24, 90}, {30, 92}, {25, 91}, {48, 114}, {49, 115}, {31, 92}, {32, 100}, {63, 123}, {44, 104}, {35, 101}, {47, 105}, {58, 124}, {60, 122}, {28, 91}, {16, 88}, {17, 89}, {41, 96}, {51, 122}, {19, 89}, {42, 96}, {52, 126}, {18, 89}, {43, 96}, {22, 90}, {45, 97}, {55, 123}, {20, 89}, {44, 97}, {23, 90}, {47, 98}, {41, 103}, {54, 120}, {21, 90}, {46, 97}, {6, 86}, {62, 110}, {51, 99}, {4, 85}, {39, 118}, {36, 117}, {7, 86}, {50, 99}, {53, 100}, {13, 95}, {48, 98}, {54, 100}, {5, 86}, {37, 118}, {49, 98}, {55, 100}, {1, 85}, {56, 108}, {13, 88}, {33, 116}, {3, 85}, {14, 88}, {59, 109}, {2, 85}, {34, 117}, {15, 88}, {9, 94}, {52, 99}, {5, 93}, {63, 103}, {50, 106}, {62, 103}, {60, 102}, {12, 87}, {61, 102}, {42, 113}, {11, 87}, {45, 113}, {43, 119}, {46, 114}, {57, 101}, {1, 92}, {10, 87}, {56, 101}, {59, 102}, {8, 86}, {9, 87}, {53, 107}, {40, 119}, {58, 101}, {14, 110}, {28, 126}, {11, 111}, {24, 125}, {10, 109}, {23, 112}, {20, 124}, {2, 107}, {7, 110}, {6, 108}, {16, 123}, {31, 116}, {30, 115}, {3, 109}, {26, 106}, {8, 121}, {17, 96}, {21, 97}, {12, 122}, {27, 108}, {40, 95}, {18, 106}, {39, 95}, {38, 95}, {36, 94}, {4, 127}, {37, 94}, {25, 98}, {3, 127}, {33, 93}, {19, 111}, {4, 120}, {2, 127}, {35, 94}, {32, 93}, {22, 107}, {1, 127}, {29, 99}, {15, 112}, {34, 93}, {9, 136}, {31, 158}, {5, 135}, {22, 149}, {30, 157}, {13, 137}, {5, 128}, {37, 160}, {6, 128}, {18, 148}, {1, 134}, {39, 160}, {7, 128}, {8, 128}, {9, 129}, {40, 161}, {11, 129}, {43, 161}, {19, 153}, {10, 129}, {14, 130}, {12, 129}, {27, 150}, {23, 154}, {15, 130}, {26, 148}, {13, 130}, {6, 150}, {29, 141}, {19, 131}, {18, 131}, {21, 132}, {11, 153}, {22, 132}, {17, 131}, {16, 130}, {55, 165}, {23, 132}, {3, 151}, {54, 162}, {15, 154}, {25, 140}, {14, 152}, {2, 149}, {20, 131}, {51, 164}, {30, 134}, {60, 164}, {28, 133}, {31, 134}, {57, 163}, {63, 165}, {61, 167}, {17, 138}, {29, 134}, {24, 132}, {25, 133}, {52, 168}, {58, 166}, {10, 151}, {21, 139}, {27, 133}, {7, 152}, {26, 133}, {42, 138}, {53, 149}, {40, 137}, {43, 138}, {41, 138}, {47, 140}, {34, 135}, {46, 139}, {4, 162}, {62, 152}, {45, 139}, {33, 135}, {50, 148}, {32, 135}, {44, 139}, {12, 164}, {8, 163}, {35, 136}, {59, 144}, {35, 143}, {36, 136}, {48, 156}, {49, 157}, {59, 151}, {60, 144}, {37, 136}, {61, 144}, {32, 142}, {63, 145}, {39, 137}, {56, 150}, {38, 137}, {62, 145}, {42, 155}, {20, 166}, {46, 156}, {28, 168}, {16, 165}, {58, 143}, {38, 144}, {45, 155}, {57, 143}, {56, 143}, {41, 145}, {54, 142}, {52, 141}, {55, 142}, {36, 159}, {53, 142}, {47, 147}, {48, 140}, {34, 159}, {49, 140}, {44, 146}, {51, 141}, {24, 167}, {33, 158}, {50, 141}, {80, 157}, {82, 159}, {81, 158}, {66, 146}, {64, 145}, {67, 146}, {65, 146}, {79, 156}, {75, 152}, {71, 148}, {72, 156}, {75, 159}, {74, 158}, {73, 157}, {70, 147}, {78, 155}, {76, 153}, {69, 147}, {68, 147}, {77, 154}, {65, 153}, {71, 155}, {72, 149}, {74, 151}, {68, 154}, {73, 150}, {66, 162}, {70, 167}, {67, 166}, {69, 163}, {64, 168}, {76, 160}, {79, 163}, {78, 162}, {77, 161}, {83, 160}, {80, 164}, {83, 167}, {82, 166}, {81, 165}, {84, 161}, {84, 168} }>;

(II) A more general form is to represent the graph as the orbit of {72, 107} under the group generated by the following permutations:

a: (97, 139)
b: (91, 133)
c: (113, 155)
d: (101, 143)
e: (109, 151)
f: (120, 162)
g: (117, 159)
h: (108, 150)
m: (110, 152)
n1: (103, 145)
a1: (98, 140)
b1: (112, 154)
c1: (111, 153)
d1: (2, 29)(3, 31)(4, 30)(5, 11)(6, 65)(7, 76)(8, 19)(9, 34)(10, 33)(12, 32)(14, 39)(15, 40)(16, 38)(17, 69)(18, 79)(20, 57)(21, 28)(22, 52)(23, 84)(24, 64)(25, 45)(26, 46)(27, 44)(35, 82)(37, 75)(41, 70)(42, 47)(43, 68)(48, 71)(49, 78)(50, 72)(51, 53)(54, 80)(55, 60)(56, 67)(59, 81)(61, 63)(62, 83)(66, 73)(85, 92)(86, 111)(87, 93)(88, 95)(89, 121)(90, 126)(91, 97)(94, 117)(96, 105)(98, 113)(99, 107)(100, 122)(101, 124)(102, 123)(103, 125)(104, 108)(106, 114)(109, 116)(110, 118)(112, 119)(115, 120)(127, 134)(128, 153)(129, 135)(130, 137)(131, 163)(132, 168)(133, 139)(136, 159)(138, 147)(140, 155)(141, 149)(142, 164)(143, 166)(144, 165)(145, 167)(146, 150)(148, 156)(151, 158)(152, 160)(154, 161)(157, 162)
e1: (106, 148)
f1: (104, 146)
g1: (124, 166)
h1: (126, 168)
m1: (115, 157)
n2: (96, 138)
a2: (86, 128)
b2: (90, 132)
c2: (121, 163)
d2: (122, 164)
e2: (123, 165)
f2: (102, 144)
g2: (92, 134)
h2: (119, 161)
m2: (88, 130)
n3: (107, 149)
a3: (118, 160)
b3: (85, 127)
c3: (125, 167)
d3: (100, 142)
e3: (94, 136)
f3: (116, 158)
g3: (99, 141)
h3: (89, 131)
m3: (114, 156)
n4: (105, 147)
a4: (1, 2, 22, 23, 77, 84, 52, 29)(3, 53, 21, 68, 40, 64, 50, 30)(4, 72, 24, 15, 43, 28, 51, 31)(5, 65, 8, 76, 7, 19, 6, 11)(9, 34, 67, 57, 37, 75, 20, 56)(10, 32, 44, 69, 39, 62, 18, 73)(12, 33, 66, 79, 83, 14, 17, 27)(13, 41, 26, 80, 74, 54, 46, 70)(16, 42, 25, 60, 81, 78, 48, 61)(35, 36, 82, 58)(38, 63, 71, 49, 59, 55, 45, 47)(85, 107, 90, 112, 119, 126, 99, 92)(86, 111)(87, 93, 104, 121, 118, 110, 89, 108)(88, 96, 91, 122, 116, 120, 114, 125)(94, 117, 124, 101)(95, 103, 106, 115, 109, 100, 97, 105)(98, 102, 123, 113)(127, 149, 132, 154, 161, 168, 141, 134)(128, 153)(129, 135, 146, 163, 160, 152, 131, 150)(130, 138, 133, 164, 158, 162, 156, 167)(136, 159, 166, 143)(137, 145, 148, 157, 151, 142, 139, 147)(140, 144, 165, 155)
b4: (2, 4)(5, 63)(6, 64)(7, 62)(8, 41)(9, 38)(10, 59)(11, 61)(12, 60)(13, 36)(14, 75)(15, 82)(16, 34)(17, 69)(18, 47)(19, 70)(20, 68)(21, 44)(22, 66)(23, 67)(24, 65)(25, 26)(27, 28)(29, 30)(32, 55)(33, 81)(35, 40)(37, 39)(42, 79)(43, 57)(45, 46)(48, 71)(49, 50)(51, 80)(52, 73)(53, 54)(56, 84)(58, 77)(72, 78)(76, 83)(86, 103)(87, 102)(88, 117)(89, 105)(90, 104)(93, 123)(94, 95)(96, 121)(98, 106)(99, 115)(101, 119)(107, 120)(108, 126)(111, 125)(112, 124)(113, 114)(128, 145)(129, 144)(130, 159)(131, 147)(132, 146)(135, 165)(136, 137)(138, 163)(140, 148)(141, 157)(143, 161)(149, 162)(150, 168)(153, 167)(154, 166)(155, 156)
c4: (93, 135)
d4: (95, 137)

(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[ 168, 60 ]
168
-1 134 92 127 85
-2 127 149 85 107
-3 127 85 151 109
-4 127 85 162 120
-5 135 93 128 86
-6 128 150 86 108
-7 110 128 86 152
-8 121 128 86 163
-9 136 94 129 87
-10 129 151 87 109
-11 111 129 87 153
-12 122 129 87 164
-13 88 137 95 130
-14 88 110 130 152
-15 88 154 112 130
-16 88 165 123 130
-17 89 138 96 131
-18 89 148 106 131
-19 89 111 131 153
-20 89 166 124 131
-21 132 90 139 97
-22 132 90 149 107
-23 132 154 90 112
-24 132 90 167 125
-25 133 91 140 98
-26 133 91 148 106
-27 133 91 150 108
-28 133 91 168 126
-29 99 134 92 141
-30 134 157 92 115
-31 134 92 158 116
-32 100 135 93 142
-33 135 158 93 116
-34 135 93 159 117
-35 143 101 136 94
-36 136 159 94 117
-37 136 94 160 118
-38 144 102 137 95
-39 137 160 95 118
-40 137 95 161 119
-41 145 103 138 96
-42 155 113 138 96
-43 138 161 96 119
-44 146 104 139 97
-45 155 113 139 97
-46 156 114 139 97
-47 147 105 140 98
-48 156 114 140 98
-49 157 115 140 98
-50 99 148 106 141
-51 99 122 141 164
-52 99 168 126 141
-53 100 149 107 142
-54 100 162 120 142
-55 165 100 123 142
-56 143 101 150 108
-57 121 143 101 163
-58 143 166 101 124
-59 144 102 151 109
-60 122 144 102 164
-61 144 167 102 125
-62 110 145 103 152
-63 165 123 145 103
-64 145 168 103 126
-65 111 146 104 153
-66 146 104 162 120
-67 166 124 146 104
-68 154 112 147 105
-69 121 147 105 163
-70 167 125 147 105
-71 155 113 148 106
-72 156 114 149 107
-73 157 115 150 108
-74 158 116 151 109
-75 110 159 117 152
-76 111 160 118 153
-77 154 112 161 119
-78 155 113 162 120
-79 121 156 114 163
-80 122 157 115 164
-81 165 123 158 116
-82 166 124 159 117
-83 167 125 160 118
-84 168 126 161 119
-85 1 2 3 4
-86 5 6 7 8
-87 11 12 9 10
-88 13 14 15 16
-89 17 18 19 20
-90 22 23 24 21
-91 25 26 27 28
-92 1 29 30 31
-93 33 34 5 32
-94 35 36 37 9
-95 13 38 39 40
-96 17 41 42 43
-97 44 45 46 21
-98 25 47 48 49
-99 50 29 51 52
-100 55 53 32 54
-101 56 35 57 58
-102 59 38 60 61
-103 62 41 63 64
-104 44 66 67 65
-105 68 47 69 70
-106 26 71 50 18
-107 22 2 72 53
-108 56 27 6 73
-109 3 59 74 10
-110 14 7 62 75
-111 11 19 65 76
-112 77 23 68 15
-113 45 78 71 42
-114 46 79 48 72
-115 80 49 73 30
-116 33 81 74 31
-117 34 36 82 75
-118 37 39 83 76
-119 77 40 84 43
-120 66 78 4 54
-121 57 79 69 8
-122 12 80 60 51
-123 55 81 16 63
-124 67 58 82 20
-125 24 70 61 83
-126 28 84 52 64
-127 1 2 3 4
-128 5 6 7 8
-129 11 12 9 10
-130 13 14 15 16
-131 17 18 19 20
-132 22 23 24 21
-133 25 26 27 28
-134 1 29 30 31
-135 33 34 5 32
-136 35 36 37 9
-137 13 38 39 40
-138 17 41 42 43
-139 44 45 46 21
-140 25 47 48 49
-141 50 29 51 52
-142 55 53 32 54
-143 56 35 57 58
-144 59 38 60 61
-145 62 41 63 64
-146 44 66 67 65
-147 68 47 69 70
-148 26 71 50 18
-149 22 2 72 53
-150 56 27 6 73
-151 3 59 74 10
-152 14 7 62 75
-153 11 19 65 76
-154 77 23 68 15
-155 45 78 71 42
-156 46 79 48 72
-157 80 49 73 30
-158 33 81 74 31
-159 34 36 82 75
-160 37 39 83 76
-161 77 40 84 43
-162 66 78 4 54
-163 57 79 69 8
-164 12 80 60 51
-165 55 81 16 63
-166 67 58 82 20
-167 24 70 61 83
-168 28 84 52 64
0

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