Non rank 3 strongly regular graphs with the 5-vertex condition
type: Item
instance of: scholarly article
title: Non rank 3 strongly regular graphs with the 5-vertex condition
zbMATH Open document ID: 0706.05056
DOI: 10.1007/BF02125894
author: Elsie Sterbin Gottlieb
published in: Combinatorica
publication date: 1989-01-01T00:00:00Z
review text: 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.
reviewed by: J.Weinstein
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 4158680
zbMATH Keywords: graph
zbMATH Keywords: t-vertex condition
zbMATH Keywords: 5-vertex condition
zbMATH Keywords: strongly regular graphs
MaRDI profile type: Publication
cites work: Q5666583
cites work: Some new strongly regular graphs
cites work: On construction and identification of graphs. With contributions by A. Lehman, G. M. Adelson-Velsky, V. Arlazarov, I. Faragev, A. Uskov, I. Zuev, M. Rosenfeld and B. Weisfeiler
cites work: Q3491802
cites work: Q3218140
cites work: PRIMITIVE AND IMPRIMITIVE GRAPHS
Recommended article: Q5488384
Recommended article: Directed strongly regular graphs with rank 5
Recommended article: 5-chromatic strongly regular graphs
Recommended article: A characterization of graphs with rank 5
Recommended article: A nonhamiltonian five-regular multitriangular polyhedral graph
Recommended article: A 1-2-3-4 result for the 1-2-3 conjecture in 5-regular graphs
Recommended article: Q3984509
Recommended article: Exceptional strongly regular graphs with eigenvalue 3
Recommended article: The strongly regular (45,\,12,\,3,\,3) graphs
description: scientific article; zbMATH DE number 4158680