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

Wai Chee SHIU, Wei Li, Wai Hong Chan

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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 λ 1 ≥ λ 2 ≥ · · · ≥ λ n. It is known that the largest eigenvalue is 3. Let R = {f i|i∈ ℤ l} be a set of l faces of a fullerene F such that f i is adjacent to f i+1, i ∈ ℤ, via an edge e i. If the edges in {e i | i ∈ ℤ l} 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 r+1 ≥ 1.

Original languageEnglish
Pages (from-to)41-51
Number of pages11
JournalAustralasian Journal of Combinatorics
Volume47
Publication statusPublished - Jun 2010

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics

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