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On this page are computer-accessible forms for the graph C4[ 240, 34 ] = PX(15,4).

(I) Following is a form readable by MAGMA:

g:=Graph<240|{ {16, 31}, {224, 239}, {208, 223}, {192, 207}, {96, 111}, {80, 95}, {32, 47}, {48, 63}, {64, 79}, {112, 127}, {128, 143}, {144, 159}, {160, 175}, {176, 191}, {1, 17}, {224, 240}, {193, 209}, {192, 208}, {97, 113}, {96, 112}, {32, 48}, {33, 49}, {64, 80}, {65, 81}, {128, 144}, {129, 145}, {160, 176}, {161, 177}, {2, 19}, {207, 222}, {194, 211}, {98, 115}, {79, 94}, {15, 30}, {34, 51}, {47, 62}, {66, 83}, {111, 126}, {130, 147}, {143, 158}, {162, 179}, {175, 190}, {14, 28}, {207, 221}, {206, 220}, {79, 93}, {78, 92}, {15, 29}, {46, 60}, {47, 61}, {110, 124}, {111, 125}, {142, 156}, {143, 157}, {174, 188}, {175, 189}, {1, 18}, {196, 215}, {193, 210}, {100, 119}, {97, 114}, {4, 23}, {33, 50}, {36, 55}, {65, 82}, {68, 87}, {129, 146}, {132, 151}, {161, 178}, {164, 183}, {12, 24}, {205, 217}, {204, 216}, {77, 89}, {76, 88}, {13, 25}, {44, 56}, {45, 57}, {108, 120}, {109, 121}, {140, 152}, {141, 153}, {172, 184}, {173, 185}, {3, 22}, {206, 219}, {195, 214}, {99, 118}, {78, 91}, {14, 27}, {35, 54}, {46, 59}, {67, 86}, {110, 123}, {131, 150}, {142, 155}, {163, 182}, {174, 187}, {2, 20}, {195, 213}, {194, 212}, {99, 117}, {98, 116}, {3, 21}, {34, 52}, {35, 53}, {66, 84}, {67, 85}, {130, 148}, {131, 149}, {162, 180}, {163, 181}, {8, 31}, {205, 218}, {200, 223}, {104, 127}, {77, 90}, {72, 95}, {13, 26}, {40, 63}, {45, 58}, {109, 122}, {136, 159}, {141, 154}, {168, 191}, {173, 186}, {9, 17}, {201, 209}, {105, 113}, {73, 81}, {41, 49}, {137, 145}, {169, 177}, {7, 30}, {202, 211}, {199, 222}, {106, 115}, {103, 126}, {74, 83}, {71, 94}, {10, 19}, {39, 62}, {42, 51}, {135, 158}, {138, 147}, {167, 190}, {170, 179}, {6, 28}, {199, 221}, {198, 220}, {103, 125}, {102, 124}, {71, 93}, {70, 92}, {7, 29}, {38, 60}, {39, 61}, {134, 156}, {135, 157}, {166, 188}, {167, 189}, {9, 18}, {204, 215}, {201, 210}, {105, 114}, {76, 87}, {73, 82}, {12, 23}, {41, 50}, {44, 55}, {108, 119}, {137, 146}, {140, 151}, {169, 178}, {172, 183}, {4, 24}, {197, 217}, {196, 216}, {101, 121}, {100, 120}, {69, 89}, {68, 88}, {5, 25}, {36, 56}, {37, 57}, {132, 152}, {133, 153}, {164, 184}, {165, 185}, {6, 27}, {203, 214}, {198, 219}, {102, 123}, {75, 86}, {70, 91}, {11, 22}, {38, 59}, {43, 54}, {107, 118}, {134, 155}, {139, 150}, {166, 187}, {171, 182}, {10, 20}, {203, 213}, {202, 212}, {106, 116}, {75, 85}, {74, 84}, {11, 21}, {42, 52}, {43, 53}, {107, 117}, {138, 148}, {139, 149}, {170, 180}, {171, 181}, {5, 26}, {197, 218}, {101, 122}, {69, 90}, {37, 58}, {133, 154}, {165, 186}, {8, 32}, {216, 240}, {200, 224}, {88, 112}, {72, 96}, {24, 48}, {136, 160}, {152, 176}, {16, 32}, {209, 225}, {208, 224}, {81, 97}, {80, 96}, {17, 33}, {144, 160}, {145, 161}, {18, 35}, {223, 238}, {210, 227}, {95, 110}, {82, 99}, {31, 46}, {146, 163}, {159, 174}, {30, 44}, {223, 237}, {222, 236}, {95, 109}, {94, 108}, {31, 45}, {158, 172}, {159, 173}, {17, 34}, {212, 231}, {209, 226}, {84, 103}, {81, 98}, {20, 39}, {145, 162}, {148, 167}, {28, 40}, {221, 233}, {220, 232}, {93, 105}, {92, 104}, {29, 41}, {156, 168}, {157, 169}, {19, 38}, {222, 235}, {211, 230}, {94, 107}, {83, 102}, {30, 43}, {147, 166}, {158, 171}, {18, 36}, {211, 229}, {210, 228}, {83, 101}, {82, 100}, {19, 37}, {146, 164}, {147, 165}, {24, 47}, {221, 234}, {216, 239}, {93, 106}, {88, 111}, {29, 42}, {152, 175}, {157, 170}, {25, 33}, {217, 225}, {89, 97}, {153, 161}, {23, 46}, {218, 227}, {215, 238}, {90, 99}, {87, 110}, {26, 35}, {151, 174}, {154, 163}, {22, 44}, {215, 237}, {214, 236}, {87, 109}, {86, 108}, {23, 45}, {150, 172}, {151, 173}, {25, 34}, {220, 231}, {217, 226}, {92, 103}, {89, 98}, {28, 39}, {153, 162}, {156, 167}, {20, 40}, {213, 233}, {212, 232}, {85, 105}, {84, 104}, {21, 41}, {148, 168}, {149, 169}, {22, 43}, {219, 230}, {214, 235}, {91, 102}, {86, 107}, {27, 38}, {150, 171}, {155, 166}, {26, 36}, {219, 229}, {218, 228}, {91, 101}, {90, 100}, {27, 37}, {154, 164}, {155, 165}, {21, 42}, {213, 234}, {85, 106}, {149, 170}, {40, 64}, {184, 208}, {56, 80}, {168, 192}, {48, 64}, {49, 65}, {176, 192}, {177, 193}, {50, 67}, {191, 206}, {63, 78}, {178, 195}, {62, 76}, {191, 205}, {190, 204}, {63, 77}, {49, 66}, {52, 71}, {177, 194}, {180, 199}, {60, 72}, {189, 201}, {188, 200}, {61, 73}, {51, 70}, {190, 203}, {62, 75}, {179, 198}, {50, 68}, {51, 69}, {178, 196}, {179, 197}, {56, 79}, {189, 202}, {184, 207}, {61, 74}, {57, 65}, {185, 193}, {55, 78}, {186, 195}, {183, 206}, {58, 67}, {54, 76}, {183, 205}, {182, 204}, {55, 77}, {57, 66}, {188, 199}, {185, 194}, {60, 71}, {52, 72}, {181, 201}, {180, 200}, {53, 73}, {54, 75}, {187, 198}, {182, 203}, {59, 70}, {58, 68}, {187, 197}, {186, 196}, {59, 69}, {53, 74}, {181, 202}, {1, 225}, {16, 240}, {3, 226}, {14, 239}, {12, 238}, {13, 239}, {2, 225}, {7, 228}, {8, 236}, {9, 237}, {6, 227}, {11, 238}, {4, 226}, {5, 227}, {10, 237}, {15, 232}, {1, 233}, {104, 128}, {120, 144}, {3, 234}, {14, 231}, {12, 230}, {13, 231}, {2, 233}, {7, 236}, {8, 228}, {9, 229}, {6, 235}, {11, 230}, {4, 234}, {5, 235}, {10, 229}, {112, 128}, {113, 129}, {114, 131}, {127, 142}, {126, 140}, {127, 141}, {113, 130}, {116, 135}, {124, 136}, {125, 137}, {115, 134}, {126, 139}, {114, 132}, {115, 133}, {120, 143}, {125, 138}, {16, 232}, {121, 129}, {119, 142}, {122, 131}, {118, 140}, {119, 141}, {121, 130}, {124, 135}, {116, 136}, {117, 137}, {118, 139}, {123, 134}, {122, 132}, {123, 133}, {15, 240}, {117, 138} }>;

(II) A more general form is to represent the graph as the orbit of {16, 31} under the group generated by the following permutations:

a: (1, 17)(2, 25)(3, 21)(4, 29)(5, 19)(6, 27)(7, 23)(8, 31)(9, 18)(10, 26)(11, 22)(12, 30)(13, 20)(14, 28)(15, 24)(16, 32)(33, 225)(34, 233)(35, 229)(36, 237)(37, 227)(38, 235)(39, 231)(40, 239)(41, 226)(42, 234)(43, 230)(44, 238)(45, 228)(46, 236)(47, 232)(48, 240)(49, 209)(50, 217)(51, 213)(52, 221)(53, 211)(54, 219)(55, 215)(56, 223)(57, 210)(58, 218)(59, 214)(60, 222)(61, 212)(62, 220)(63, 216)(64, 224)(65, 193)(66, 201)(67, 197)(68, 205)(69, 195)(70, 203)(71, 199)(72, 207)(73, 194)(74, 202)(75, 198)(76, 206)(77, 196)(78, 204)(79, 200)(80, 208)(81, 177)(82, 185)(83, 181)(84, 189)(85, 179)(86, 187)(87, 183)(88, 191)(89, 178)(90, 186)(91, 182)(92, 190)(93, 180)(94, 188)(95, 184)(96, 192)(97, 161)(98, 169)(99, 165)(100, 173)(101, 163)(102, 171)(103, 167)(104, 175)(105, 162)(106, 170)(107, 166)(108, 174)(109, 164)(110, 172)(111, 168)(112, 176)(113, 145)(114, 153)(115, 149)(116, 157)(117, 147)(118, 155)(119, 151)(120, 159)(121, 146)(122, 154)(123, 150)(124, 158)(125, 148)(126, 156)(127, 152)(128, 160)(130, 137)(131, 133)(132, 141)(134, 139)(136, 143)(140, 142)
b: (2, 9)(3, 5)(4, 13)(6, 11)(8, 15)(12, 14)(17, 225)(18, 233)(19, 229)(20, 237)(21, 227)(22, 235)(23, 231)(24, 239)(25, 226)(26, 234)(27, 230)(28, 238)(29, 228)(30, 236)(31, 232)(32, 240)(33, 209)(34, 217)(35, 213)(36, 221)(37, 211)(38, 219)(39, 215)(40, 223)(41, 210)(42, 218)(43, 214)(44, 222)(45, 212)(46, 220)(47, 216)(48, 224)(49, 193)(50, 201)(51, 197)(52, 205)(53, 195)(54, 203)(55, 199)(56, 207)(57, 194)(58, 202)(59, 198)(60, 206)(61, 196)(62, 204)(63, 200)(64, 208)(65, 177)(66, 185)(67, 181)(68, 189)(69, 179)(70, 187)(71, 183)(72, 191)(73, 178)(74, 186)(75, 182)(76, 190)(77, 180)(78, 188)(79, 184)(80, 192)(81, 161)(82, 169)(83, 165)(84, 173)(85, 163)(86, 171)(87, 167)(88, 175)(89, 162)(90, 170)(91, 166)(92, 174)(93, 164)(94, 172)(95, 168)(96, 176)(97, 145)(98, 153)(99, 149)(100, 157)(101, 147)(102, 155)(103, 151)(104, 159)(105, 146)(106, 154)(107, 150)(108, 158)(109, 148)(110, 156)(111, 152)(112, 160)(113, 129)(114, 137)(115, 133)(116, 141)(117, 131)(118, 139)(119, 135)(120, 143)(121, 130)(122, 138)(123, 134)(124, 142)(125, 132)(126, 140)(127, 136)(128, 144)
c: (1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(225, 226)(227, 228)(229, 230)(231, 232)(233, 234)(235, 236)(237, 238)(239, 240)
d: (81, 82)(83, 84)(85, 86)(87, 88)(89, 90)(91, 92)(93, 94)(95, 96)(97, 99)(98, 100)(101, 103)(102, 104)(105, 107)(106, 108)(109, 111)(110, 112)(113, 117)(114, 118)(115, 119)(116, 120)(121, 125)(122, 126)(123, 127)(124, 128)(129, 137)(130, 138)(131, 139)(132, 140)(133, 141)(134, 142)(135, 143)(136, 144)
e: (177, 178)(179, 180)(181, 182)(183, 184)(185, 186)(187, 188)(189, 190)(191, 192)(193, 195)(194, 196)(197, 199)(198, 200)(201, 203)(202, 204)(205, 207)(206, 208)(209, 213)(210, 214)(211, 215)(212, 216)(217, 221)(218, 222)(219, 223)(220, 224)(225, 233)(226, 234)(227, 235)(228, 236)(229, 237)(230, 238)(231, 239)(232, 240)
f: (97, 98)(99, 100)(101, 102)(103, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 115)(114, 116)(117, 119)(118, 120)(121, 123)(122, 124)(125, 127)(126, 128)(129, 133)(130, 134)(131, 135)(132, 136)(137, 141)(138, 142)(139, 143)(140, 144)(145, 153)(146, 154)(147, 155)(148, 156)(149, 157)(150, 158)(151, 159)(152, 160)
g: (113, 114)(115, 116)(117, 118)(119, 120)(121, 122)(123, 124)(125, 126)(127, 128)(129, 131)(130, 132)(133, 135)(134, 136)(137, 139)(138, 140)(141, 143)(142, 144)(145, 149)(146, 150)(147, 151)(148, 152)(153, 157)(154, 158)(155, 159)(156, 160)(161, 169)(162, 170)(163, 171)(164, 172)(165, 173)(166, 174)(167, 175)(168, 176)
h: (33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)(49, 51)(50, 52)(53, 55)(54, 56)(57, 59)(58, 60)(61, 63)(62, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 77)(74, 78)(75, 79)(76, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)
m: (49, 50)(51, 52)(53, 54)(55, 56)(57, 58)(59, 60)(61, 62)(63, 64)(65, 67)(66, 68)(69, 71)(70, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)
n1: (65, 66)(67, 68)(69, 70)(71, 72)(73, 74)(75, 76)(77, 78)(79, 80)(81, 83)(82, 84)(85, 87)(86, 88)(89, 91)(90, 92)(93, 95)(94, 96)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128)
a1: (145, 146)(147, 148)(149, 150)(151, 152)(153, 154)(155, 156)(157, 158)(159, 160)(161, 163)(162, 164)(165, 167)(166, 168)(169, 171)(170, 172)(173, 175)(174, 176)(177, 181)(178, 182)(179, 183)(180, 184)(185, 189)(186, 190)(187, 191)(188, 192)(193, 201)(194, 202)(195, 203)(196, 204)(197, 205)(198, 206)(199, 207)(200, 208)
b1: (129, 130)(131, 132)(133, 134)(135, 136)(137, 138)(139, 140)(141, 142)(143, 144)(145, 147)(146, 148)(149, 151)(150, 152)(153, 155)(154, 156)(157, 159)(158, 160)(161, 165)(162, 166)(163, 167)(164, 168)(169, 173)(170, 174)(171, 175)(172, 176)(177, 185)(178, 186)(179, 187)(180, 188)(181, 189)(182, 190)(183, 191)(184, 192)
c1: (161, 162)(163, 164)(165, 166)(167, 168)(169, 170)(171, 172)(173, 174)(175, 176)(177, 179)(178, 180)(181, 183)(182, 184)(185, 187)(186, 188)(189, 191)(190, 192)(193, 197)(194, 198)(195, 199)(196, 200)(201, 205)(202, 206)(203, 207)(204, 208)(209, 217)(210, 218)(211, 219)(212, 220)(213, 221)(214, 222)(215, 223)(216, 224)
d1: (17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)
e1: (1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)

(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[ 240, 34 ]
240
-1 233 225 17 18
-2 233 225 19 20
-3 22 234 226 21
-4 23 24 234 226
-5 25 26 235 227
-6 235 27 28 227
-7 236 29 30 228
-8 236 228 31 32
-9 17 237 18 229
-10 237 19 20 229
-11 22 238 21 230
-12 23 24 238 230
-13 231 25 26 239
-14 231 27 28 239
-15 232 29 30 240
-16 232 31 240 32
-17 33 1 34 9
-18 1 35 36 9
-19 2 37 38 10
-20 2 39 40 10
-21 11 3 41 42
-22 11 44 3 43
-23 12 45 46 4
-24 12 47 4 48
-25 33 34 13 5
-26 13 35 36 5
-27 14 37 38 6
-28 14 6 39 40
-29 15 7 41 42
-30 44 15 7 43
-31 45 46 16 8
-32 47 48 16 8
-33 25 49 17 50
-34 25 17 51 52
-35 26 18 53 54
-36 55 56 26 18
-37 57 58 27 19
-38 59 27 60 19
-39 28 61 62 20
-40 28 63 20 64
-41 49 50 29 21
-42 29 51 52 21
-43 22 30 53 54
-44 22 55 56 30
-45 23 57 58 31
-46 23 59 60 31
-47 24 61 62 32
-48 24 63 64 32
-49 33 66 41 65
-50 33 67 68 41
-51 34 69 70 42
-52 34 71 72 42
-53 35 73 74 43
-54 35 75 43 76
-55 44 77 78 36
-56 44 79 36 80
-57 66 45 37 65
-58 45 67 68 37
-59 46 69 70 38
-60 46 38 71 72
-61 47 39 73 74
-62 47 39 75 76
-63 77 78 48 40
-64 79 80 48 40
-65 57 81 49 82
-66 57 49 83 84
-67 58 50 85 86
-68 88 58 50 87
-69 89 90 59 51
-70 91 59 92 51
-71 60 93 94 52
-72 60 95 52 96
-73 81 82 61 53
-74 61 83 84 53
-75 62 85 86 54
-76 88 62 54 87
-77 55 89 90 63
-78 55 91 92 63
-79 56 93 94 64
-80 56 95 96 64
-81 73 97 65 98
-82 99 100 73 65
-83 66 101 102 74
-84 66 103 104 74
-85 67 105 106 75
-86 67 107 75 108
-87 110 68 76 109
-88 111 68 112 76
-89 77 69 97 98
-90 77 99 100 69
-91 78 101 102 70
-92 78 70 103 104
-93 79 71 105 106
-94 79 71 107 108
-95 110 80 72 109
-96 111 112 80 72
-97 89 113 81 114
-98 89 81 115 116
-99 90 82 117 118
-100 90 82 119 120
-101 121 122 91 83
-102 123 91 124 83
-103 92 125 126 84
-104 92 127 84 128
-105 113 114 93 85
-106 93 115 116 85
-107 94 117 118 86
-108 94 86 119 120
-109 121 122 95 87
-110 123 124 95 87
-111 88 125 126 96
-112 88 127 128 96
-113 105 129 97 130
-114 132 105 97 131
-115 133 134 106 98
-116 135 136 106 98
-117 99 137 138 107
-118 99 139 107 140
-119 100 108 141 142
-120 143 100 144 108
-121 101 129 130 109
-122 132 101 109 131
-123 110 133 134 102
-124 110 102 135 136
-125 111 103 137 138
-126 111 103 139 140
-127 112 104 141 142
-128 143 144 112 104
-129 121 145 113 146
-130 121 113 147 148
-131 122 114 149 150
-132 122 114 151 152
-133 154 123 115 153
-134 155 123 156 115
-135 124 157 158 116
-136 124 159 116 160
-137 145 146 125 117
-138 125 147 148 117
-139 126 149 150 118
-140 126 118 151 152
-141 154 127 119 153
-142 155 156 127 119
-143 157 158 128 120
-144 159 160 128 120
-145 137 161 129 162
-146 137 129 163 164
-147 165 166 138 130
-148 167 168 138 130
-149 169 170 139 131
-150 171 139 172 131
-151 132 140 173 174
-152 132 176 140 175
-153 133 161 162 141
-154 133 141 163 164
-155 165 166 134 142
-156 134 167 168 142
-157 143 135 169 170
-158 143 135 171 172
-159 144 136 173 174
-160 176 144 136 175
-161 177 145 178 153
-162 145 179 180 153
-163 154 146 181 182
-164 154 146 183 184
-165 155 147 185 186
-166 187 155 188 147
-167 156 189 190 148
-168 156 191 148 192
-169 177 178 157 149
-170 157 179 180 149
-171 158 181 182 150
-172 158 150 183 184
-173 159 151 185 186
-174 187 188 159 151
-175 189 190 160 152
-176 191 192 160 152
-177 169 193 161 194
-178 169 161 195 196
-179 198 170 162 197
-180 199 200 170 162
-181 201 202 171 163
-182 203 171 204 163
-183 172 205 206 164
-184 172 207 164 208
-185 165 193 194 173
-186 165 173 195 196
-187 198 166 174 197
-188 166 199 200 174
-189 167 201 202 175
-190 167 203 204 175
-191 176 168 205 206
-192 176 168 207 208
-193 209 177 210 185
-194 177 211 212 185
-195 178 213 214 186
-196 178 215 216 186
-197 187 179 217 218
-198 187 220 179 219
-199 188 221 222 180
-200 188 223 180 224
-201 209 210 189 181
-202 189 211 212 181
-203 190 213 214 182
-204 190 182 215 216
-205 191 183 217 218
-206 220 191 183 219
-207 221 222 192 184
-208 223 224 192 184
-209 201 225 193 226
-210 201 193 227 228
-211 202 194 229 230
-212 231 232 202 194
-213 233 234 203 195
-214 235 203 236 195
-215 204 237 238 196
-216 204 239 196 240
-217 225 226 205 197
-218 205 227 228 197
-219 198 206 229 230
-220 198 231 232 206
-221 199 233 234 207
-222 199 235 236 207
-223 200 237 238 208
-224 200 239 240 208
-225 209 1 2 217
-226 209 3 4 217
-227 210 5 6 218
-228 210 7 8 218
-229 211 9 10 219
-230 11 12 211 219
-231 220 13 14 212
-232 220 212 15 16
-233 1 221 2 213
-234 221 3 4 213
-235 222 5 214 6
-236 222 214 7 8
-237 223 215 9 10
-238 11 12 223 215
-239 13 14 224 216
-240 15 224 16 216
0

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