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On this page are computer-accessible forms for the graph C4[ 176, 10 ] = SDD(W(22,2)).

(I) Following is a form readable by MAGMA:

g:=Graph<176|{ {80, 89}, {80, 90}, {80, 91}, {81, 92}, {80, 94}, {77, 94}, {66, 90}, {85, 117}, {66, 102}, {78, 107}, {65, 104}, {82, 123}, {83, 127}, {66, 111}, {88, 118}, {76, 126}, {77, 127}, {79, 122}, {83, 102}, {81, 100}, {75, 125}, {78, 121}, {81, 104}, {77, 119}, {88, 98}, {45, 109}, {52, 118}, {58, 126}, {36, 98}, {57, 126}, {45, 100}, {51, 122}, {32, 106}, {44, 103}, {34, 110}, {33, 108}, {52, 121}, {36, 107}, {37, 116}, {48, 97}, {49, 96}, {12, 94}, {35, 113}, {13, 95}, {38, 117}, {40, 123}, {40, 124}, {36, 113}, {45, 120}, {11, 93}, {63, 105}, {36, 114}, {51, 101}, {42, 125}, {52, 99}, {1, 89}, {32, 120}, {49, 105}, {1, 91}, {6, 92}, {43, 113}, {48, 106}, {55, 109}, {1, 90}, {2, 89}, {3, 95}, {39, 123}, {33, 125}, {44, 112}, {41, 116}, {4, 90}, {34, 124}, {5, 91}, {45, 115}, {57, 103}, {1, 94}, {3, 92}, {2, 93}, {13, 109}, {19, 115}, {14, 111}, {28, 125}, {2, 96}, {29, 127}, {25, 123}, {24, 122}, {6, 100}, {5, 103}, {4, 102}, {3, 97}, {20, 119}, {8, 108}, {22, 114}, {20, 112}, {10, 110}, {9, 109}, {57, 93}, {7, 98}, {25, 124}, {16, 118}, {26, 124}, {19, 117}, {17, 118}, {17, 121}, {18, 122}, {49, 89}, {55, 95}, {3, 106}, {2, 105}, {8, 99}, {4, 111}, {7, 107}, {11, 103}, {48, 92}, {49, 93}, {9, 100}, {21, 120}, {6, 104}, {23, 121}, {15, 97}, {14, 96}, {10, 101}, {27, 116}, {48, 95}, {28, 108}, {9, 120}, {16, 98}, {19, 97}, {17, 99}, {12, 127}, {20, 96}, {26, 110}, {5, 112}, {27, 110}, {22, 99}, {11, 126}, {7, 114}, {7, 113}, {31, 105}, {30, 104}, {18, 101}, {44, 91}, {14, 119}, {8, 114}, {22, 108}, {15, 117}, {9, 115}, {12, 119}, {29, 102}, {20, 111}, {15, 115}, {23, 107}, {10, 116}, {27, 101}, {14, 112}, {21, 106}, {8, 136}, {4, 134}, {39, 165}, {6, 132}, {5, 135}, {10, 137}, {31, 156}, {23, 147}, {29, 153}, {30, 155}, {37, 160}, {29, 155}, {38, 161}, {47, 168}, {21, 157}, {41, 160}, {46, 167}, {39, 172}, {24, 148}, {60, 176}, {28, 144}, {42, 166}, {13, 128}, {15, 129}, {25, 150}, {63, 176}, {42, 165}, {61, 173}, {11, 154}, {62, 175}, {16, 130}, {27, 137}, {19, 129}, {17, 131}, {13, 158}, {24, 140}, {24, 141}, {26, 143}, {59, 174}, {26, 140}, {59, 173}, {18, 133}, {28, 139}, {25, 142}, {51, 164}, {31, 135}, {58, 162}, {50, 168}, {50, 169}, {23, 139}, {54, 170}, {53, 168}, {62, 163}, {61, 160}, {22, 136}, {21, 138}, {62, 161}, {30, 129}, {56, 167}, {35, 131}, {53, 148}, {38, 132}, {53, 150}, {63, 156}, {57, 154}, {60, 159}, {41, 141}, {61, 152}, {40, 142}, {46, 136}, {47, 137}, {58, 156}, {59, 157}, {60, 154}, {50, 149}, {37, 141}, {43, 131}, {54, 158}, {55, 158}, {32, 138}, {33, 139}, {44, 135}, {56, 147}, {58, 145}, {34, 143}, {34, 140}, {54, 152}, {12, 163}, {31, 176}, {56, 151}, {56, 136}, {30, 175}, {33, 144}, {16, 162}, {39, 149}, {35, 145}, {43, 159}, {18, 164}, {51, 133}, {37, 146}, {52, 131}, {55, 128}, {61, 133}, {63, 135}, {62, 134}, {46, 151}, {47, 150}, {43, 145}, {41, 146}, {47, 148}, {59, 128}, {35, 159}, {53, 137}, {54, 138}, {32, 157}, {42, 151}, {46, 147}, {50, 143}, {40, 150}, {60, 130}, {38, 153}, {65, 129}, {71, 133}, {79, 141}, {79, 140}, {66, 134}, {78, 139}, {87, 146}, {72, 142}, {82, 149}, {83, 155}, {86, 159}, {64, 138}, {83, 153}, {74, 128}, {68, 143}, {85, 153}, {86, 154}, {67, 142}, {76, 156}, {68, 149}, {85, 132}, {84, 134}, {70, 146}, {86, 130}, {69, 144}, {81, 132}, {74, 157}, {64, 152}, {73, 144}, {65, 155}, {88, 130}, {79, 148}, {75, 151}, {76, 145}, {78, 147}, {64, 158}, {71, 152}, {72, 169}, {69, 167}, {73, 171}, {70, 164}, {72, 171}, {74, 174}, {67, 166}, {73, 172}, {86, 176}, {71, 160}, {74, 173}, {67, 171}, {70, 174}, {69, 172}, {64, 170}, {71, 173}, {67, 169}, {68, 168}, {70, 170}, {68, 169}, {75, 166}, {65, 175}, {77, 163}, {76, 162}, {75, 165}, {73, 167}, {72, 166}, {69, 171}, {87, 164}, {85, 161}, {84, 161}, {82, 165}, {84, 163}, {87, 174}, {88, 162}, {84, 175}, {87, 170}, {82, 172} }>;

(II) A more general form is to represent the graph as the orbit of {80, 89} under the group generated by the following permutations:

a: (35, 43)
b: (28, 46)(33, 56)(108, 136)(125, 151)(139, 147)(144, 167)
c: (16, 35)(43, 88)(98, 113)(118, 131)(130, 159)(145, 162)
d: (21, 32)
e: (47, 53)
f: (62, 84)
g: (39, 67)(72, 82)(123, 142)(149, 169)(165, 166)(171, 172)
h: (67, 72)
m: (29, 62)(83, 84)(102, 134)(127, 163)(153, 161)(155, 175)
n1: (25, 40)
a1: (59, 74)
b1: (70, 87)
c1: (15, 19)
d1: (2, 4)(3, 7)(5, 12)(6, 16)(8, 13)(9, 17)(10, 25)(11, 29)(15, 35)(18, 39)(19, 43)(21, 23)(22, 55)(24, 50)(27, 40)(28, 54)(30, 58)(31, 62)(32, 78)(33, 64)(36, 48)(37, 67)(38, 60)(41, 72)(42, 61)(44, 77)(45, 52)(46, 59)(49, 66)(51, 82)(56, 74)(57, 83)(63, 84)(65, 76)(68, 79)(69, 70)(71, 75)(73, 87)(81, 88)(85, 86)(89, 90)(91, 94)(92, 98)(93, 102)(95, 114)(96, 111)(97, 113)(99, 109)(100, 118)(101, 123)(103, 127)(104, 162)(105, 134)(106, 107)(108, 158)(110, 124)(112, 119)(115, 131)(116, 142)(117, 159)(120, 121)(122, 149)(125, 152)(126, 155)(128, 136)(129, 145)(130, 132)(133, 165)(135, 163)(137, 150)(138, 139)(140, 143)(141, 169)(144, 170)(146, 171)(147, 157)(148, 168)(151, 173)(153, 154)(156, 175)(160, 166)(161, 176)(164, 172)(167, 174)
e1: (13, 21)(32, 55)(95, 106)(109, 120)(128, 157)(138, 158)
f1: (26, 34)
g1: (30, 38)(65, 85)(104, 132)(117, 129)(153, 155)(161, 175)
h1: (60, 86)
m1: (8, 22)
n2: (37, 41)
a2: (18, 37)(41, 51)(101, 116)(122, 141)(133, 160)(146, 164)
b2: (31, 63)
c2: (38, 85)
d2: (25, 50)(40, 68)(123, 149)(124, 143)(142, 169)(150, 168)
e2: (3, 9)(45, 48)(92, 100)(95, 109)(97, 115)(106, 120)
f2: (50, 68)
g2: (4, 12)(66, 77)(90, 94)(102, 127)(111, 119)(134, 163)
h2: (1, 2)(3, 8)(4, 11)(5, 14)(6, 7)(9, 23)(10, 26)(12, 31)(13, 28)(15, 17)(16, 30)(18, 25)(19, 52)(20, 44)(21, 46)(22, 48)(24, 47)(27, 34)(29, 58)(32, 56)(33, 55)(35, 38)(36, 81)(37, 50)(39, 61)(40, 51)(41, 68)(42, 54)(43, 85)(45, 78)(49, 80)(53, 79)(57, 66)(59, 69)(60, 62)(63, 77)(64, 75)(65, 88)(67, 70)(71, 82)(72, 87)(73, 74)(76, 83)(84, 86)(90, 93)(91, 96)(92, 114)(94, 105)(95, 108)(97, 99)(98, 104)(100, 107)(101, 124)(102, 126)(103, 111)(106, 136)(109, 139)(113, 132)(115, 121)(116, 143)(117, 131)(118, 129)(119, 135)(120, 147)(122, 150)(123, 133)(125, 158)(127, 156)(128, 144)(130, 175)(134, 154)(137, 140)(138, 151)(141, 168)(142, 164)(145, 153)(146, 169)(149, 160)(152, 165)(155, 162)(157, 167)(159, 161)(163, 176)(166, 170)(171, 174)(172, 173)
m2: (54, 59)(64, 74)(128, 158)(138, 157)(152, 173)(170, 174)
n3: (5, 44)
a3: (7, 17)(36, 52)(98, 118)(99, 114)(107, 121)(113, 131)
b3: (12, 77)
c3: (14, 20)
d3: (23, 78)
e3: (9, 45)
f3: (26, 47)(34, 53)(110, 137)(124, 150)(140, 148)(143, 168)
g3: (11, 31)(57, 63)(93, 105)(103, 135)(126, 156)(154, 176)
h3: (24, 79)
m3: (17, 52)
n4: (58, 60)(76, 86)(126, 154)(130, 162)(145, 159)(156, 176)
a4: (6, 15)(19, 81)(92, 97)(100, 115)(104, 129)(117, 132)
b4: (69, 73)
c4: (46, 56)
d4: (42, 69)(73, 75)(125, 144)(151, 167)(165, 172)(166, 171)
e4: (61, 70)(71, 87)(133, 164)(146, 160)(152, 170)(173, 174)
f4: (8, 23)(22, 78)(99, 121)(107, 114)(108, 139)(136, 147)
g4: (28, 33)
h4: (10, 24)(27, 79)(101, 122)(110, 140)(116, 141)(137, 148)

(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[ 176, 10 ]
176
-1 89 90 91 94
-2 89 93 105 96
-3 92 95 106 97
-4 111 90 134 102
-5 112 91 135 103
-6 132 100 92 104
-7 113 114 107 98
-8 99 114 136 108
-9 100 115 109 120
-10 110 101 137 116
-11 154 103 93 126
-12 94 127 119 163
-13 158 95 128 109
-14 111 112 96 119
-15 115 117 129 97
-16 118 162 130 98
-17 99 121 118 131
-18 122 133 101 164
-19 115 117 129 97
-20 111 112 96 119
-21 157 138 106 120
-22 99 114 136 108
-23 121 147 139 107
-24 122 148 140 141
-25 123 124 150 142
-26 110 143 124 140
-27 110 101 137 116
-28 144 125 139 108
-29 155 102 127 153
-30 155 104 129 175
-31 176 156 135 105
-32 157 138 106 120
-33 144 125 139 108
-34 110 143 124 140
-35 145 113 159 131
-36 113 114 107 98
-37 146 116 160 141
-38 132 117 161 153
-39 165 123 149 172
-40 123 124 150 142
-41 146 116 160 141
-42 165 166 125 151
-43 145 113 159 131
-44 112 91 135 103
-45 100 115 109 120
-46 167 136 147 151
-47 168 137 148 150
-48 92 95 106 97
-49 89 93 105 96
-50 143 168 169 149
-51 122 133 101 164
-52 99 121 118 131
-53 168 137 148 150
-54 158 170 138 152
-55 158 95 128 109
-56 167 136 147 151
-57 154 103 93 126
-58 145 156 126 162
-59 157 128 173 174
-60 154 176 159 130
-61 133 160 173 152
-62 134 161 163 175
-63 176 156 135 105
-64 158 170 138 152
-65 155 104 129 175
-66 111 90 134 102
-67 166 169 171 142
-68 143 168 169 149
-69 144 167 171 172
-70 146 170 174 164
-71 133 160 173 152
-72 166 169 171 142
-73 144 167 171 172
-74 157 128 173 174
-75 165 166 125 151
-76 145 156 126 162
-77 94 127 119 163
-78 121 147 139 107
-79 122 148 140 141
-80 89 90 91 94
-81 132 100 92 104
-82 165 123 149 172
-83 155 102 127 153
-84 134 161 163 175
-85 132 117 161 153
-86 154 176 159 130
-87 146 170 174 164
-88 118 162 130 98
-89 1 2 80 49
-90 66 1 80 4
-91 44 1 80 5
-92 3 48 81 6
-93 11 2 57 49
-94 77 1 12 80
-95 55 13 3 48
-96 2 14 49 20
-97 3 15 48 19
-98 88 36 16 7
-99 22 17 8 52
-100 45 81 6 9
-101 27 18 51 10
-102 66 4 83 29
-103 11 44 57 5
-104 81 6 30 65
-105 2 49 63 31
-106 3 48 21 32
-107 23 78 36 7
-108 22 33 28 8
-109 55 45 13 9
-110 34 26 27 10
-111 66 14 4 20
-112 44 14 5 20
-113 35 36 7 43
-114 22 36 7 8
-115 45 15 19 9
-116 37 27 41 10
-117 15 38 19 85
-118 88 16 17 52
-119 77 12 14 20
-120 45 9 21 32
-121 23 78 17 52
-122 24 79 18 51
-123 25 82 39 40
-124 34 25 26 40
-125 33 28 42 75
-126 11 57 58 76
-127 77 12 83 29
-128 55 13 59 74
-129 15 19 30 65
-130 88 16 60 86
-131 35 17 52 43
-132 81 38 6 85
-133 71 61 18 51
-134 66 4 62 84
-135 44 5 63 31
-136 22 56 46 8
-137 47 27 53 10
-138 64 21 32 54
-139 33 23 78 28
-140 34 24 79 26
-141 24 79 37 41
-142 67 25 72 40
-143 34 68 26 50
-144 33 69 28 73
-145 35 58 43 76
-146 37 70 41 87
-147 23 56 78 46
-148 24 79 47 53
-149 68 82 39 50
-150 25 47 40 53
-151 56 46 42 75
-152 71 61 64 54
-153 38 83 29 85
-154 11 57 60 86
-155 83 29 30 65
-156 58 63 31 76
-157 59 74 21 32
-158 55 13 64 54
-159 35 60 86 43
-160 37 71 61 41
-161 38 62 84 85
-162 88 58 16 76
-163 77 12 62 84
-164 70 18 51 87
-165 82 39 42 75
-166 67 72 42 75
-167 56 46 69 73
-168 68 47 50 53
-169 67 68 50 72
-170 70 64 54 87
-171 67 69 72 73
-172 69 82 39 73
-173 59 71 61 74
-174 59 70 74 87
-175 62 84 30 65
-176 60 63 31 86
0

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