Anton Koval

A strongly regular graph with parameters (217,66,15,22)

We construct a strongly regular graph with parameters (217,66,15,22), and hence one with the complementary parameters (217,150,105,100). Both parameter sets were marked "?" (existence unknown) in Brouwer's online table on 18 October 2026, with the remark that they are the paramet...

There is no strongly regular graph with parameters (196,81,42,27)

We prove that no strongly regular graph with parameters (196,81,42,27) exists, and hence none with the complementary parameters (196,114,59,76); in particular there is no partial geometry pg(6,18,4) (and none with the dual parameters pg(18,6,4)). Brouwer's table lists the paramet...

The strongly regular graphs with parameters (243,110,37,60) and (253,112,36,60) are unique

We prove that the Delsarte graph is the only strongly regular graph with parameters (243,110,37,60), and that the M23 graph on the 253 heptads of the Steiner system S(4,7,23) is the only strongly regular graph with parameters (253,112,36,60). Hence the complementary parameter set...

There is no strongly regular graph with parameters (476,133,60,28)

We prove that no strongly regular graph with parameters (476,133,60,28) exists, and hence none with the complementary parameters (476,342,236,270). Brouwer's table lists this parameter set as open, and Koolen and Gebremichel list it among the twelve open primitive parameter sets...

On the local structure of a hypothetical strongly regular graph with parameters (99,14,1,2)

Conway asked whether there is a graph on 99 vertices in which every edge lies in a unique triangle and every non-edge is the diagonal of a unique quadrilateral, i.e. a strongly regular graph srg(99,14,1,2). This paper does NOT decide that question. It proves structural restrictio...

There is no strongly regular graph with parameters (405,132,63,33)

We prove that no strongly regular graph with parameters (405,132,63,33) exists. Brouwer's table lists this parameter set as open, and its complement (405,272,172,204) as the putative point graph of a partial geometry pg(8,33,6); Koolen and Gebremichel list it among the twelve ope...