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On this page are computer-accessible forms for the graph C4[ 72, 9 ] = R_36(20,19).

(I) Following is a form readable by MAGMA:

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

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

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

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