Non rank 3 strongly regular graphs with the 5-vertex condition
The concept of a graph satisfying the t-vertex condition for some natural number \(t\geq 2\) was introduced and studied in previous work by the author [Darstellungstheorie endlicher Gruppen, Math. Forschungsinstitut Oberwolfach, Tagungsbericht 24, 8-9 (1987)], the author and \textit{M. H. Klin} [Proc. XIXth All-Union Alg. Conf., Part 2, L'vov, 104 (1987)], and by \textit{M. H. Klin} and \textit{I. A. Faradjev} [Investigations on applied graph theory, Collect. Artic., Novosibirsk 1986, 59-97 (1986; Zbl 0659.20004)]; it generalizes some of the concepts investigated by \textit{M. D. Hestenes} and \textit{D. G. Higman} [Computers Algebra, Number Theory, Proc. Sympos. Appl. Math. Amer. math. Soc. and Soc. industr. appl. Math. 1970, SIAM-AMS Proc. 4, 141-160 (1971; Zbl 0253.05127)]. In the present paper, the author describes a graph on 256 vertices which satisfies the 5-vertex condition and two of its subgraphs on 120 and 135 vertices which satisfy the weaker 4-vertex condition. These three graphs are the first examples of strongly regular graphs with the 4-vertex condition which are not rank 3 graphs.
scientific article; zbMATH DE number 4158680