On cliques in edge-regular graphs

被引：11

作者：

Soicher, Leonard H. ^{[1
]}

机构：

[1] Queen Mary Univ London, Sch Math Sci, London E1 4NS, England

来源：

JOURNAL OF ALGEBRA | 2015年 / 421卷

关键词：

Edge-regular graph; Orbital graph; Strongly regular graph; Clique; Maximum clique; Regular clique; Quasiregular clique; Delsarte bound; Hoffman bound; Partial geometry;

D O I：

10.1016/j.jalgebra.2014.08.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma be an edge-regular graph with given parameters (v, k, lambda). We show how to apply a certain "block intersection polynomial" in two variables to determine a good upper bound on the clique number of Gamma, and to obtain further information concerning the cliques S of Gamma with the property that every vertex of Gamma not in S is adjacent to exactly m or m + 1 vertices of S, for some constant m >= 0. Some interesting examples are studied using computation with groups and graphs. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：260 / 267

页数：8

共 13 条

[1]

[Anonymous], 2007, HDB COMBINATORIAL DE

[2]

[Anonymous], 2012, GRAPE PACKAGE GAP VE

[3]

Bailey R. A., 2009, Surveys in combinatorics 2009, V365, P19

[4] STRONGLY REGULAR GRAPHS, PARTIAL GEOMETRIES AND PARTIALLY BALANCED DESIGNS [J].

BOSE, RC .

PACIFIC JOURNAL OF MATHEMATICS, 1963, 13 (02) :389-&

[5]

Brouwer A.E., 1989, Distance-Regular Graphs

[6] Block intersection polynomials [J].

Cameron, Peter J. ;

Soicher, Leonard H. .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2007, 39 :559-564

[7]

Delsarte P, 1973, PHILIPS RES REP S, V10

[8]

Faradzev I. A., 1994, INVESTIGATIONS ALGEB, P1, DOI DOI 10.1007/978-94-017-1972-8

[9]

Haemers W. H., 1996, Designs, Codes and Cryptography, V8, P145, DOI 10.1007/BF00130574

[10]

Neumaier A., 1981, LONDON MATH SOC LECT, V49, P244

← 1 2 →