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On this page are computer-accessible forms for the graph C4[ 152, 6 ] = SDD(W(19,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 101} under the group generated by the following permutations:

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

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

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