Walk regular divisible design graphs
Crnkovic,Dean Haemers,W. H.
Crnkovic,Dean
Haemers,W. H.
Abstract
A divisible design graph (DDG for short) is a graph whose adjacency matrix is the incidence matrix of a divisible design. DDGs were introduced by Kharaghani, Meulenberg and the second author as a generalization of (v,k,\lambda )-graphs. It turns out that most (but not all) of the known examples of DDGs are walk-regular. In this paper we present an easy criterion for this to happen. In several cases walk-regularity is forced by the parameters of the DDG; then known conditions for walk-regularity lead to nonexistence results for DDGs. In addition, we construct some new DDGs, and check old and new constructions for walk-regularity. In doing so, we present and use special properties in case the classes have size two. All feasible parameter sets for DDGs on at most 27 vertices are examined. Existence is established in all but one case, and existence of a walk-regular DDG in all cases
Description
Date
2014-07
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
Organizational Units
Journal Issue
Keywords
divisible design graph, divisible design, walk-regular graph, Hadamard matrix
Citation
Crnkovic, D & Haemers, W H 2014, 'Walk regular divisible design graphs', Designs Codes and Cryptography, vol. 72, no. 1, pp. 165-175. https://doi.org/10.1007/s10623-013-9861-0
License
info:eu-repo/semantics/closedAccess