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On this page are computer-accessible forms for the graph C4[ 84, 18 ] = B(L(F28)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {35, 55} under the group generated by the following permutations:

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

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

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