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On this page are computer-accessible forms for the graph C4[ 72, 10 ] = R_36(29,10).

(I) Following is a form readable by MAGMA:

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

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

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