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On this page are computer-accessible forms for the graph C4[ 80, 12 ] = MPS(4,40;9).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 45} under the group generated by the following permutations:

a: (4, 49)(14, 59)(23, 68)(33, 78)
b: (5, 50)(15, 60)(24, 69)(34, 79)
c: (3, 48)(13, 58)(22, 67)(32, 77)
d: (1, 2)(3, 10)(4, 9)(5, 8)(6, 7)(11, 12)(13, 20)(14, 19)(15, 18)(16, 17)(22, 75)(23, 29)(24, 28)(25, 27)(30, 77)(32, 65)(33, 39)(34, 38)(35, 37)(40, 67)(41, 52)(42, 51)(43, 50)(44, 49)(45, 48)(46, 57)(47, 56)(53, 60)(54, 59)(55, 58)(61, 71)(62, 70)(63, 69)(64, 68)(66, 76)(72, 80)(73, 79)(74, 78)
e: (9, 19)(28, 73)(29, 64)(38, 63)(39, 74)(44, 54)
f: (10, 45)(20, 55)(30, 65)(40, 75)
g: (8, 18)(27, 72)(28, 63)(37, 62)(38, 73)(43, 53)
h: (7, 17)(26, 71)(27, 62)(36, 61)(37, 72)(42, 52)
m: (2, 10)(3, 9)(4, 8)(5, 7)(12, 20)(13, 19)(14, 18)(15, 17)(21, 75)(22, 29)(23, 28)(24, 27)(25, 26)(30, 76)(31, 65)(32, 39)(33, 38)(34, 37)(35, 36)(40, 66)(41, 51)(42, 50)(43, 49)(44, 48)(45, 47)(46, 56)(52, 60)(53, 59)(54, 58)(55, 57)(61, 70)(62, 69)(63, 68)(64, 67)(71, 80)(72, 79)(73, 78)(74, 77)
n1: (1, 21, 2, 22, 3, 23, 4, 24, 5, 25, 6, 26, 7, 27, 8, 28, 9, 29, 10, 30, 11, 31, 12, 32, 13, 33, 14, 34, 15, 35, 16, 36, 17, 37, 18, 38, 19, 39, 20, 40)(41, 71, 42, 72, 43, 73, 44, 74, 45, 75, 46, 76, 47, 77, 48, 78, 49, 79, 50, 80, 51, 61, 52, 62, 53, 63, 54, 64, 55, 65, 56, 66, 57, 67, 58, 68, 59, 69, 60, 70)
a1: (6, 16)(25, 70)(26, 61)(35, 80)(36, 71)(41, 51)
b1: (7, 42)(17, 52)(27, 62)(37, 72)
c1: (8, 43)(18, 53)(28, 63)(38, 73)
d1: (9, 44)(19, 54)(29, 64)(39, 74)
e1: (6, 41)(16, 51)(26, 61)(36, 71)
f1: (10, 20)(29, 74)(30, 65)(39, 64)(40, 75)(45, 55)
g1: (5, 15)(24, 69)(25, 80)(34, 79)(35, 70)(50, 60)
h1: (4, 14)(23, 68)(24, 79)(33, 78)(34, 69)(49, 59)
m1: (3, 13)(22, 67)(23, 78)(32, 77)(33, 68)(48, 58)

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

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