On \(k\)-walk-regular graphs
type: Item
instance of: scholarly article
title: On \(k\)-walk-regular graphs
zbMATH Open document ID: 1226.05107
author: C. Dalfó
author: E. Garriga
author: Miquel Angel Fiol
published in: The Electronic Journal of Combinatorics
publication date: 2009-07-08T00:00:00Z
full work available at URL: https://eudml.org/doc/117510
full work available at URL: v16i1r47.html
review text: Summary: Considering a connected graph \(G\) with diameter \(D\), we say that it is \(k\)-walk-regular, for a given integer \(k\) (\(0\leq k \leq D\)), if the number of walks of length \(\ell\) between any pair of vertices only depends on the distance between them, provided that this distance does not exceed \(k\). Thus, for \(k=0\), this definition coincides with that of walk-regular graph, where the number of cycles of length \(\ell\) rooted at a given vertex is a constant through all the graph. In the other extreme, for \(k=D\), we get one of the possible definitions for a graph to be distance-regular. In this paper we show some algebraic characterizations of \(k\)-walk-regularity, which are based on the so-called local spectrum and predistance polynomials of \(G\).
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5576428
zbMATH Keywords: algebraic characterizations of \(k\)-walk-regularity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5576428