Isoperimetric numbers of graph bundles
type: Item
instance of: scholarly article
title: Isoperimetric numbers of graph bundles
zbMATH Open document ID: 0865.05050
DOI: 10.1007/BF01858458
author: Jaeun Lee
author: Moo Young Sohn
author: Jin Ho Kwak
published in: Graphs and Combinatorics
publication date: 1997-06-29T00:00:00Z
review text: The isoperimetric number of a graph \(G\) is, roughly speaking, the minimum ratio \(|\partial X|/|X|\) of the size of a cocycle in \(G\) to the number of vertices in the smaller of the two parts of \(G-\partial X\). This invariant has been extensively studied in the recent years, see \textit{B. Mohar} [J. Comb. Theory, Ser. B 47, No. 3, 274-291 (1989; Zbl 0719.05042)]. The paper under review is devoted to upper and lower bounds of the isoperimetric number of a graph bundle. Graph bundle is a common generalization of a graph covering projection and the Cartesian product of graphs. The authors show that the isoperimetric number of any covering graph is not greater than that of the base graph. A more detailed evaluation is given in the case when the fibre is the complete graph. This extends a result of Mohar (loc. cit.) concerning the isoperimetric number of the Cartesian product of a graph and a complete graph.
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 934037
zbMATH Keywords: isoperimetric number
zbMATH Keywords: graph bundle
zbMATH Keywords: covering projection
zbMATH Keywords: Cartesian product
zbMATH Keywords: covering graph
reviewed by: Martin Škoviera
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 934037