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On this page are computer-accessible forms for the graph C4[ 120, 56 ] = SDD(W(15,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {11, 63} under the group generated by the following permutations:

a: (54, 55)
b: (28, 30)(31, 33)(85, 86)(87, 88)(93, 96)(94, 95)
c: (26, 27)
d: (13, 15)
e: (2, 5)(4, 8)(6, 11)(9, 14)(10, 16)(13, 18)(15, 19)(17, 21)(20, 24)(22, 26)(23, 27)(25, 29)(28, 32)(30, 34)(31, 35)(33, 37)(36, 40)(38, 42)(39, 43)(41, 45)(44, 48)(46, 50)(47, 51)(49, 53)(52, 56)(54, 58)(55, 59)(57, 60)(61, 63)(62, 65)(64, 68)(66, 71)(67, 72)(69, 74)(70, 75)(73, 77)(76, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(93, 97)(94, 98)(95, 99)(96, 100)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(118, 120)
f: (32, 34)(35, 37)(89, 90)(91, 92)(97, 100)(98, 99)
g: (44, 46)(47, 49)(101, 102)(103, 104)(109, 112)(110, 111)
h: (1, 2)(3, 6)(4, 7)(5, 10)(8, 13)(9, 12)(11, 17)(14, 15)(16, 20)(18, 22)(19, 23)(21, 25)(24, 28)(26, 30)(27, 31)(29, 33)(32, 36)(34, 38)(35, 39)(37, 41)(40, 44)(42, 46)(43, 47)(45, 49)(48, 52)(50, 54)(51, 55)(53, 57)(62, 64)(63, 66)(65, 69)(68, 73)(70, 72)(71, 76)(74, 78)(75, 79)(77, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 117)(114, 118)(115, 119)(116, 120)
m: (50, 51)
n1: (56, 58)(59, 60)(113, 114)(115, 116)(117, 118)(119, 120)
a1: (46, 47)
b1: (10, 13)(15, 17)(66, 69)(70, 73)(76, 80)(78, 79)
c1: (16, 18)(19, 21)(71, 74)(75, 77)(81, 84)(82, 83)
d1: (34, 35)
e1: (7, 12)
f1: (4, 9)
g1: (8, 14)
h1: (38, 39)
m1: (48, 50)(51, 53)(105, 106)(107, 108)(113, 116)(114, 115)
n2: (58, 59)
a2: (5, 8)(11, 14)(63, 65)(68, 72)(71, 77)(74, 75)
b2: (22, 23)
c2: (40, 42)(43, 45)(97, 98)(99, 100)(105, 108)(106, 107)
d2: (52, 54)(55, 57)(109, 110)(111, 112)(117, 120)(118, 119)
e2: (42, 43)
f2: (36, 38)(39, 41)(93, 94)(95, 96)(101, 104)(102, 103)
g2: (18, 19)
h2: (30, 31)
m2: (24, 26)(27, 29)(81, 82)(83, 84)(89, 92)(90, 91)
n3: (2, 4)(6, 9)(61, 62)(64, 67)(66, 73)(69, 70)
a3: (20, 22)(23, 25)(76, 78)(79, 80)(85, 88)(86, 87)

(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[ 120, 56 ]
120
-1 61 62 63 65
-2 66 69 61 64
-3 61 62 63 65
-4 67 70 62 73
-5 68 71 63 74
-6 66 69 61 64
-7 67 68 72 64
-8 77 72 75 65
-9 67 70 62 73
-10 66 78 73 76
-11 68 71 63 74
-12 67 68 72 64
-13 79 69 80 70
-14 77 72 75 65
-15 79 69 80 70
-16 77 81 71 82
-17 66 78 73 76
-18 83 84 74 75
-19 83 84 74 75
-20 80 85 86 76
-21 77 81 71 82
-22 88 78 79 87
-23 88 78 79 87
-24 89 90 81 84
-25 80 85 86 76
-26 91 92 82 83
-27 91 92 82 83
-28 88 93 94 85
-29 89 90 81 84
-30 95 96 86 87
-31 95 96 86 87
-32 89 92 97 98
-33 88 93 94 85
-34 99 100 90 91
-35 99 100 90 91
-36 101 102 93 96
-37 89 92 97 98
-38 103 104 94 95
-39 103 104 94 95
-40 100 105 106 97
-41 101 102 93 96
-42 99 107 108 98
-43 99 107 108 98
-44 110 101 104 109
-45 100 105 106 97
-46 111 112 102 103
-47 111 112 102 103
-48 113 114 105 108
-49 110 101 104 109
-50 115 116 106 107
-51 115 116 106 107
-52 112 117 118 109
-53 113 114 105 108
-54 110 111 119 120
-55 110 111 119 120
-56 113 116 117 120
-57 112 117 118 109
-58 114 115 118 119
-59 114 115 118 119
-60 113 116 117 120
-61 1 2 3 6
-62 1 3 4 9
-63 11 1 3 5
-64 12 2 6 7
-65 1 3 14 8
-66 2 6 17 10
-67 12 4 7 9
-68 11 12 5 7
-69 2 13 15 6
-70 13 4 15 9
-71 11 5 16 21
-72 12 14 7 8
-73 4 17 9 10
-74 11 5 18 19
-75 14 18 8 19
-76 25 17 20 10
-77 14 16 8 21
-78 22 23 17 10
-79 22 23 13 15
-80 13 25 15 20
-81 24 16 29 21
-82 26 16 27 21
-83 26 27 18 19
-84 24 18 29 19
-85 33 25 28 20
-86 25 30 20 31
-87 22 23 30 31
-88 22 33 23 28
-89 24 37 29 32
-90 34 24 35 29
-91 34 35 26 27
-92 26 37 27 32
-93 33 36 28 41
-94 33 38 28 39
-95 38 39 30 31
-96 36 30 41 31
-97 45 37 40 32
-98 37 42 32 43
-99 34 35 42 43
-100 34 45 35 40
-101 44 36 49 41
-102 46 36 47 41
-103 46 47 38 39
-104 44 38 49 39
-105 45 48 40 53
-106 45 50 40 51
-107 50 51 42 43
-108 48 42 53 43
-109 44 57 49 52
-110 44 55 49 54
-111 55 46 47 54
-112 46 57 47 52
-113 56 48 60 53
-114 58 48 59 53
-115 58 59 50 51
-116 56 60 50 51
-117 56 57 60 52
-118 57 58 59 52
-119 55 58 59 54
-120 55 56 60 54
0

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