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On this page are computer-accessible forms for the graph C4[ 84, 19 ] = UG(Rmap(168,16){8,4|6}_14).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {38, 39} under the group generated by the following permutations:

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

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

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