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On this page are computer-accessible forms for the graph C4[ 144, 14 ] = MPS(4,72;17).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 73} under the group generated by the following permutations:

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

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

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