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On this page are computer-accessible forms for the graph C4[ 168, 54 ] = UG(Rmap(336,307){8,4|6}_28).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {38, 39} under the group generated by the following permutations:

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

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

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