Strongly regular graphs on 100 - 199 vertices

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Parameters for strongly regular graphs on 100-199 vertices

The fields in the following table are all straightforward. The parameters are given in the standard (n,k,a,c) fashion. The eigenvalues of the adjacency matrix are called theta and tau with respective multiplicities m_theta and m_tau .

The Number field (will eventually) give some indication of the number of graphs known, the Type field indicates if the graph is a conference graph or a Smith graph (one of the Krein conditions is tight). Any further comments will be linked into the final column.

Parameters theta m_theta tau m_tau Number Type Comments
(100, 18, 8, 2) 8 18 -2 81 ?   none yet
(100, 22, 0, 6) 2 77 -8 22 ? Smith none yet
(100, 27, 10, 6) 7 27 -3 72 ?   none yet
(100, 33, 8, 12) 3 66 -7 33 ?   none yet
(100, 33, 14, 9) 8 24 -3 75 ?   none yet
(100, 36, 14, 12) 6 36 -4 63 ?   none yet
(100, 44, 18, 20) 4 55 -6 44 ?   none yet
(100, 45, 20, 20) 5 45 -5 54 ?   none yet
(101, 50, 24, 25) 4.525 50 -5.525 50 ? Conf. none yet
(105, 26, 13, 4) 11 14 -2 90 ?   none yet
(105, 32, 4, 12) 2 84 -10 20 ?   none yet
(105, 40, 15, 15) 5 48 -5 56 ?   none yet
(105, 52, 21, 30) 2 84 -11 20 ?   none yet
(105, 52, 29, 22) 10 20 -3 84 ?   none yet
(109, 54, 26, 27) 4.720 54 -5.720 54 ? Conf. none yet
(111, 30, 5, 9) 3 74 -7 36 ?   none yet
(111, 44, 19, 16) 7 36 -4 74 ?   none yet
(112, 30, 2, 10) 2 90 -10 21 ? Smith none yet
(112, 36, 10, 12) 4 63 -6 48 ?   none yet
(113, 56, 27, 28) 4.815 56 -5.815 56 ? Conf. none yet
(115, 18, 1, 3) 3 69 -5 45 ?   none yet
(117, 36, 15, 9) 9 26 -3 90 ?   none yet
(117, 58, 28, 29) 4.908 58 -5.908 58 ? Conf. none yet
(119, 54, 21, 27) 3 84 -9 34 ?   none yet
(120, 28, 14, 4) 12 15 -2 104 ?   none yet
(120, 34, 8, 10) 4 68 -6 51 ?   none yet
(120, 35, 10, 10) 5 56 -5 63 ?   none yet
(120, 42, 8, 18) 2 99 -12 20 ?   none yet
(120, 51, 18, 24) 3 85 -9 34 ?   none yet
(120, 56, 28, 24) 8 35 -4 84 ?   none yet
(121, 20, 9, 2) 9 20 -2 100 ?   none yet
(121, 30, 11, 6) 8 30 -3 90 ?   none yet
(121, 36, 7, 12) 3 84 -8 36 ?   none yet
(121, 40, 15, 12) 7 40 -4 80 ?   none yet
(121, 48, 17, 20) 4 72 -7 48 ?   none yet
(121, 50, 21, 20) 6 50 -5 70 ?   none yet
(121, 60, 29, 30) 5.000 60 -6.000 60 ? Conf. none yet
(122, 55, 24, 25) 5 61 -6 60 ?   none yet
(125, 28, 3, 7) 3 84 -7 40 ?   none yet
(125, 52, 15, 26) 2 104 -13 20 ?   none yet
(125, 62, 30, 31) 5.090 62 -6.090 62 ? Conf. none yet
(126, 25, 8, 4) 7 35 -3 90 ?   none yet
(126, 45, 12, 18) 3 90 -9 35 ?   none yet
(126, 50, 13, 24) 2 105 -13 20 ?   none yet
(126, 60, 33, 24) 12 21 -3 104 ?   none yet
(130, 48, 20, 16) 8 39 -4 90 ?   none yet
(133, 24, 5, 4) 5 56 -4 76 ?   none yet
(133, 32, 6, 8) 4 76 -6 56 ?   none yet
(133, 44, 15, 14) 6 56 -5 76 ?   none yet
(135, 64, 28, 32) 4 84 -8 50 ?   none yet
(136, 30, 8, 6) 6 51 -4 84 ?   none yet
(136, 30, 15, 4) 13 16 -2 119 ?   none yet
(136, 60, 24, 28) 4 85 -8 50 ?   none yet
(136, 63, 30, 28) 7 51 -5 84 ?   none yet
(137, 68, 33, 34) 5.352 68 -6.352 68 ? Conf. none yet
(143, 70, 33, 35) 5 77 -7 65 ?   none yet
(144, 22, 10, 2) 10 22 -2 121 ?   none yet
(144, 33, 12, 6) 9 33 -3 110 ?   none yet
(144, 39, 6, 12) 3 104 -9 39 ?   none yet
(144, 44, 16, 12) 8 44 -4 99 ?   none yet
(144, 52, 16, 20) 4 91 -8 52 ?   none yet
(144, 55, 22, 20) 7 55 -5 88 ?   none yet
(144, 65, 28, 30) 5 78 -7 65 ?   none yet
(144, 66, 30, 30) 6 66 -6 77 ?   none yet
(145, 72, 35, 36) 5.521 72 -6.521 72 ? Conf. none yet
(147, 66, 25, 33) 3 110 -11 36 ?   none yet
(148, 63, 22, 30) 3 111 -11 36 ?   none yet
(148, 70, 36, 30) 10 37 -4 110 ?   none yet
(149, 74, 36, 37) 5.603 74 -6.603 74 ? Conf. none yet
(153, 32, 16, 4) 14 17 -2 135 ?   none yet
(153, 56, 19, 21) 5 84 -7 68 ?   none yet
(153, 76, 37, 38) 5.685 76 -6.685 76 ? Conf. none yet
(154, 48, 12, 16) 4 98 -8 55 ?   none yet
(154, 72, 26, 40) 2 132 -16 21 ?   none yet
(155, 42, 17, 9) 11 30 -3 124 ?   none yet
(156, 30, 4, 6) 4 90 -6 65 ?   none yet
(157, 78, 38, 39) 5.765 78 -6.765 78 ? Conf. none yet
(160, 54, 18, 18) 6 75 -6 84 ?   none yet
(162, 21, 0, 3) 3 105 -6 56 ?   none yet
(162, 23, 4, 3) 5 69 -4 92 ?   none yet
(162, 49, 16, 14) 7 63 -5 98 ?   none yet
(162, 56, 10, 24) 2 140 -16 21 ? Smith none yet
(162, 69, 36, 24) 15 23 -3 138 ?   none yet
(165, 36, 3, 9) 3 120 -9 44 ?   none yet
(169, 24, 11, 2) 11 24 -2 144 ?   none yet
(169, 36, 13, 6) 10 36 -3 132 ?   none yet
(169, 42, 5, 12) 3 126 -10 42 ?   none yet
(169, 48, 17, 12) 9 48 -4 120 ?   none yet
(169, 56, 15, 20) 4 112 -9 56 ?   none yet
(169, 60, 23, 20) 8 60 -5 108 ?   none yet
(169, 70, 27, 30) 5 98 -8 70 ?   none yet
(169, 72, 31, 30) 7 72 -6 96 ?   none yet
(169, 84, 41, 42) 6.000 84 -7.000 84 ? Conf. none yet
(170, 78, 35, 36) 6 85 -7 84 ?   none yet
(171, 34, 17, 4) 15 18 -2 152 ?   none yet
(171, 50, 13, 15) 5 95 -7 75 ?   none yet
(171, 60, 15, 24) 3 132 -12 38 ?   none yet
(173, 86, 42, 43) 6.076 86 -7.076 86 ? Conf. none yet
(175, 30, 5, 5) 5 84 -5 90 ?   none yet
(175, 66, 29, 22) 11 42 -4 132 ?   none yet
(175, 72, 20, 36) 2 153 -18 21 ?   none yet
(176, 25, 0, 4) 3 120 -7 55 ?   none yet
(176, 40, 12, 8) 8 55 -4 120 ?   none yet
(176, 45, 18, 9) 12 32 -3 143 ?   none yet
(176, 49, 12, 14) 5 98 -7 77 ?   none yet
(176, 70, 18, 34) 2 154 -18 21 ?   none yet
(176, 70, 24, 30) 4 120 -10 55 ?   none yet
(176, 85, 48, 34) 17 22 -3 153 ?   none yet
(181, 90, 44, 45) 6.227 90 -7.227 90 ? Conf. none yet
(183, 52, 11, 16) 4 122 -9 60 ?   none yet
(183, 70, 29, 25) 9 60 -5 122 ?   none yet
(185, 92, 45, 46) 6.301 92 -7.301 92 ? Conf. none yet
(189, 48, 12, 12) 6 90 -6 98 ?   none yet
(189, 60, 27, 15) 15 28 -3 160 ?   none yet
(189, 88, 37, 44) 4 132 -11 56 ?   none yet
(190, 36, 18, 4) 16 19 -2 170 ?   none yet
(190, 45, 12, 10) 7 75 -5 114 ?   none yet
(190, 84, 33, 40) 4 133 -11 56 ?   none yet
(190, 84, 38, 36) 8 75 -6 114 ?   none yet
(190, 90, 45, 40) 10 57 -5 132 ?   none yet
(193, 96, 47, 48) 6.446 96 -7.446 96 ? Conf. none yet
(195, 96, 46, 48) 6 104 -8 90 ?   none yet
(196, 26, 12, 2) 12 26 -2 169 ?   none yet
(196, 39, 2, 9) 3 147 -10 48 ?   none yet
(196, 39, 14, 6) 11 39 -3 156 ?   none yet
(196, 45, 4, 12) 3 150 -11 45 ?   none yet
(196, 52, 18, 12) 10 52 -4 143 ?   none yet
(196, 60, 14, 20) 4 135 -10 60 ?   none yet
(196, 60, 23, 16) 11 48 -4 147 ?   none yet
(196, 65, 24, 20) 9 65 -5 130 ?   none yet
(196, 75, 26, 30) 5 120 -9 75 ?   none yet
(196, 78, 32, 30) 8 78 -6 117 ?   none yet
(196, 81, 42, 27) 18 24 -3 171 ?   none yet
(196, 90, 40, 42) 6 105 -8 90 ?   none yet
(196, 91, 42, 42) 7 91 -7 104 ?   none yet
(197, 98, 48, 49) 6.518 98 -7.518 98 ? Conf. none yet