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On this page are computer-accessible forms for the graph C4[ 90, 6 ] = PS(6,15;4).

(I) Following is a form readable by MAGMA:

g:=Graph<90|{ {45, 46}, {27, 31}, {59, 63}, {58, 62}, {57, 61}, {75, 76}, {20, 31}, {52, 63}, {51, 62}, {32, 46}, {65, 79}, {64, 78}, {33, 47}, {50, 61}, {1, 17}, {74, 90}, {73, 89}, {72, 88}, {71, 87}, {70, 86}, {69, 85}, {68, 84}, {67, 83}, {66, 82}, {65, 81}, {64, 80}, {44, 60}, {43, 59}, {42, 58}, {41, 57}, {40, 56}, {39, 55}, {14, 30}, {13, 29}, {12, 28}, {11, 27}, {10, 26}, {9, 25}, {8, 24}, {7, 23}, {6, 22}, {5, 21}, {4, 20}, {3, 19}, {2, 18}, {32, 48}, {33, 49}, {34, 50}, {35, 51}, {36, 52}, {37, 53}, {38, 54}, {2, 16}, {75, 89}, {74, 88}, {71, 85}, {70, 84}, {67, 81}, {66, 80}, {43, 57}, {42, 56}, {39, 53}, {15, 29}, {14, 28}, {11, 25}, {10, 24}, {7, 21}, {6, 20}, {3, 17}, {34, 48}, {35, 49}, {38, 52}, {4, 18}, {69, 83}, {68, 82}, {45, 59}, {44, 58}, {13, 27}, {12, 26}, {5, 19}, {36, 50}, {37, 51}, {8, 22}, {73, 87}, {72, 86}, {41, 55}, {40, 54}, {9, 23}, {1, 30}, {15, 16}, {31, 60}, {31, 47}, {16, 35}, {20, 39}, {24, 43}, {17, 36}, {19, 38}, {21, 32}, {23, 34}, {25, 44}, {29, 40}, {18, 37}, {22, 33}, {26, 45}, {30, 41}, {16, 42}, {17, 43}, {24, 35}, {28, 39}, {28, 32}, {29, 33}, {30, 34}, {21, 40}, {23, 42}, {25, 36}, {27, 38}, {18, 44}, {19, 45}, {22, 41}, {26, 37}, {12, 76}, {15, 79}, {14, 78}, {13, 77}, {8, 79}, {5, 76}, {7, 78}, {6, 77}, {1, 80}, {11, 90}, {9, 88}, {7, 86}, {5, 84}, {3, 82}, {2, 81}, {10, 89}, {6, 85}, {1, 87}, {4, 83}, {9, 80}, {15, 86}, {13, 84}, {11, 82}, {2, 88}, {3, 89}, {10, 81}, {14, 85}, {4, 90}, {8, 87}, {12, 83}, {46, 72}, {47, 73}, {61, 90}, {47, 66}, {46, 65}, {61, 77}, {63, 79}, {62, 78}, {62, 76}, {63, 77}, {48, 67}, {56, 75}, {52, 71}, {49, 68}, {55, 66}, {53, 64}, {51, 70}, {50, 69}, {54, 65}, {48, 74}, {49, 75}, {56, 67}, {60, 71}, {60, 64}, {53, 72}, {59, 70}, {57, 68}, {55, 74}, {54, 73}, {58, 69} }>;

(II) A more general form is to represent the graph as the orbit of {45, 46} under the group generated by the following permutations:

a: (2, 12)(3, 8)(5, 15)(6, 11)(9, 14)(16, 76)(17, 87)(18, 83)(19, 79)(20, 90)(21, 86)(22, 82)(23, 78)(24, 89)(25, 85)(26, 81)(27, 77)(28, 88)(29, 84)(30, 80)(31, 61)(32, 72)(33, 68)(34, 64)(35, 75)(36, 71)(37, 67)(38, 63)(39, 74)(40, 70)(41, 66)(42, 62)(43, 73)(44, 69)(45, 65)(47, 57)(48, 53)(50, 60)(51, 56)(54, 59)
b: (1, 2)(3, 15)(4, 14)(5, 13)(6, 12)(7, 11)(8, 10)(16, 17)(18, 30)(19, 29)(20, 28)(21, 27)(22, 26)(23, 25)(31, 32)(33, 45)(34, 44)(35, 43)(36, 42)(37, 41)(38, 40)(46, 47)(48, 60)(49, 59)(50, 58)(51, 57)(52, 56)(53, 55)(61, 62)(63, 75)(64, 74)(65, 73)(66, 72)(67, 71)(68, 70)(76, 77)(78, 90)(79, 89)(80, 88)(81, 87)(82, 86)(83, 85)
c: (2, 5)(3, 9)(4, 13)(7, 10)(8, 14)(12, 15)(16, 76)(17, 80)(18, 84)(19, 88)(20, 77)(21, 81)(22, 85)(23, 89)(24, 78)(25, 82)(26, 86)(27, 90)(28, 79)(29, 83)(30, 87)(31, 61)(32, 65)(33, 69)(34, 73)(35, 62)(36, 66)(37, 70)(38, 74)(39, 63)(40, 67)(41, 71)(42, 75)(43, 64)(44, 68)(45, 72)(47, 50)(48, 54)(49, 58)(52, 55)(53, 59)(57, 60)
d: (2, 37)(3, 73)(5, 40)(6, 61)(8, 43)(9, 64)(11, 31)(12, 67)(14, 34)(15, 70)(16, 51)(17, 87)(19, 54)(20, 90)(22, 57)(23, 78)(25, 60)(26, 81)(28, 48)(29, 84)(33, 68)(36, 71)(39, 74)(42, 62)(45, 65)(47, 82)(50, 85)(53, 88)(56, 76)(59, 79)
e: (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90)(46, 61)(47, 62)(48, 63)(49, 64)(50, 65)(51, 66)(52, 67)(53, 68)(54, 69)(55, 70)(56, 71)(57, 72)(58, 73)(59, 74)(60, 75)

(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[ 90, 6 ]
90
-1 80 17 30 87
-2 88 81 16 18
-3 89 82 17 19
-4 90 83 18 20
-5 84 19 21 76
-6 22 77 85 20
-7 23 78 86 21
-8 22 24 79 87
-9 88 23 25 80
-10 89 24 26 81
-11 90 25 27 82
-12 26 28 83 76
-13 77 27 29 84
-14 78 28 30 85
-15 79 16 29 86
-16 2 35 15 42
-17 1 3 36 43
-18 44 2 4 37
-19 45 3 5 38
-20 4 6 39 31
-21 5 7 40 32
-22 33 6 8 41
-23 34 7 9 42
-24 35 8 10 43
-25 11 44 36 9
-26 12 45 37 10
-27 11 13 38 31
-28 12 14 39 32
-29 33 13 15 40
-30 1 34 14 41
-31 47 27 60 20
-32 46 48 28 21
-33 22 47 49 29
-34 23 48 50 30
-35 24 16 49 51
-36 25 17 50 52
-37 26 18 51 53
-38 27 19 52 54
-39 55 28 20 53
-40 56 29 21 54
-41 22 55 57 30
-42 23 56 58 16
-43 24 57 59 17
-44 25 58 60 18
-45 46 26 59 19
-46 45 72 32 65
-47 33 66 73 31
-48 34 67 74 32
-49 33 35 68 75
-50 34 36 69 61
-51 35 37 70 62
-52 36 38 71 63
-53 37 39 72 64
-54 38 40 73 65
-55 66 39 41 74
-56 67 40 42 75
-57 68 61 41 43
-58 44 69 62 42
-59 45 70 63 43
-60 44 71 31 64
-61 77 57 90 50
-62 78 58 51 76
-63 77 79 59 52
-64 78 80 60 53
-65 46 79 81 54
-66 55 47 80 82
-67 56 48 81 83
-68 57 49 82 84
-69 58 50 83 85
-70 59 51 84 86
-71 60 52 85 87
-72 88 46 53 86
-73 89 47 54 87
-74 55 88 90 48
-75 56 89 49 76
-76 12 5 62 75
-77 13 6 61 63
-78 14 7 62 64
-79 15 8 63 65
-80 66 1 9 64
-81 67 2 10 65
-82 11 66 68 3
-83 12 67 69 4
-84 13 68 70 5
-85 14 69 71 6
-86 15 70 72 7
-87 1 71 73 8
-88 2 72 74 9
-89 3 73 75 10
-90 11 4 61 74
0

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