Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property
type: Item
instance of: scholarly article
title: Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property
zbMATH Open document ID: 0955.05068
author: Anthony Bonato
author: W. H. Holzmann
author: H. Kharaghani
published in: The Electronic Journal of Combinatorics
publication date: 2001-01-09T00:00:00Z
full work available at URL: https://eudml.org/doc/120786
full work available at URL: v8i1r1.html
review text: Summary: A graph is \(3\)-e.c. if for every \(3\)-element subset \(S\) of the vertices, and for every subset \(T\) of \(S\), there is a vertex not in \(S\) which is joined to every vertex in \(T\) and to no vertex in \(S\setminus T\). Although almost all graphs are \(3\)-e.c., the only known examples of strongly regular \(3\)-e.c. graphs are Paley graphs with at least \(29\) vertices. We construct a new infinite family of \(3\)-e.c. graphs, based on certain Hadamard matrices, that are strongly regular but not Paley graphs. Specifically, we show that Bush-type Hadamard matrices of order \(16n^2\) give rise to strongly regular \(3\)-e.c. graphs, for each odd \(n\) for which \(4n\) is the order of a Hadamard matrix.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1549892
zbMATH Keywords: \(n\)-e.c. graphs
zbMATH Keywords: Bush-type Hadamard matrix
zbMATH Keywords: design
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1549892