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On this page are computer-accessible forms for the graph C4[ 72, 3 ] = C_72(1,19).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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