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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Maximal resonance of cubic bipartite polyhedral graphs

Language

English

Abstract

Let H be a set of disjoint faces of a cubic bipartite polyhedral graph G. If G has a perfect matching M such that the boundary of each face of H is an M-alternating cycle (or in other words, G - H has a perfect matching), then H is called a resonant pattern of G. Furthermore, G is k-resonant if every i (1 ≤ i ≤ k) disjoint faces of G form a resonant pattern. In particular, G is called maximally resonant if G is k-resonant for all integers k ≥ 1. In this paper, all the cubic bipartite polyhedral graphs, which are maximally resonant, are characterized. As a corollary, it is shown that if a cubic bipartite polyhedral graph is 3-resonant then it must be maximally resonant. However, 2-resonant ones need not to be maximally resonant. © 2010 Springer Science+Business Media, LLC.

Keywords

Cyclical edge-connectivity, k-resonant, Polyhedral graph

Publication Date

2010

Source Publication Title

Journal of Mathematical Chemistry

Volume

48

Issue

3

Start Page

676

End Page

686

Publisher

Springer Verlag

ISSN (print)

02599791

ISSN (electronic)

15728897

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