On the spectra of the fullerenes that contain a nontrivial cyclic-5-cutset

Wai Chee SHIU, Wei LI, Wai Hong CHAN

Research output: Contribution to journalArticles

3 Citations (Scopus)

Abstract

A fullerene, which is a 3-connected cubic plane graph whose faces are pentagons and hexagons, is cyclically 5 edge-connected. For a fullerene of order n, it is customary to index the eigenvalues in non-increasing order λ₁ ≥ λ₂ ≥ ∙∙∙ ≥ λn. It is known that the largest eigenvalue is 3. Let R = {fi|i ϵ Zl} be a set of l faces of a fullerene F such that fi is adjacent to fi ₊₁, i ϵ Zl, via an edge ei. If the edges in { ei| i ϵ Zl} are independent, then we say that R forms a ring of l faces. In this paper we show that if a fullerene contains a nontrivial cyclic-5-cutset, then it has 2r ─ 2 eigenvalues that can be arranged in pairs {μ, ─ μ} (1 < μ < 3), where r is the number of the rings of five faces. Meanwhile 1 is one of its eigenvalues and λ₊₁ ≥ 1. Copyright © 2010 American Scholars Press Inc.
Original languageEnglish
Pages (from-to)41-51
JournalAustralasian Journal of Combinatorics
Volume47
Publication statusPublished - Jun 2010

Citation

Shiu, W. C., Li, W., & Chan, W. H. (2010). On the spectra of the fullerenes that contain a nontrivial cyclic-5-cutset. Australasian Journal of Combinatorics, 47, 41-51.

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