✦ LIBER ✦

Some results on the Laplacian spectrum

✍ Scribed by Muhuo Liu; Bolian Liu

Book ID: 104008861
Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 290 KB
Volume: 59
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.03.058

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✦ Synopsis

A graph is called a Laplacian integral graph if the spectrum of its Laplacian matrix consists of integers, and a graph G is said to be determined by its Laplacian spectrum if there does not exist other non-isomorphic graph H such that H and G share the same Laplacian spectrum. In this paper, we obtain a sharp upper bound for the algebraic connectivity of a graph, and identify all the Laplacian integral unicyclic, bicyclic graphs. Moreover, we show that all the Laplacian integral unicyclic, bicyclic graphs are determined by their Laplacian spectra.

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