Laplacian spectral characterization of some graph products

Suijie Wang; Xiaogang Liu

doi:10.1016/j.laa.2012.05.003

paper

Laplacian spectral characterization of some graph products

arXiv:1007.2472 · doi:10.1016/j.laa.2012.05.003

Abstract

This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: $G = G : ∣ E G ∣ \leq ∣ V G ∣ + 1$ , and characterize all graphs $G \in G$ such that the products $G \times K_{m}$ are $L$ -DS graphs. The main result of this paper states that, if $G \in G$ , except for $C_{6}$ and $Θ_{3, 2, 5}$ , is $L$ -DS graph, so is the product $G \times K_{m}$ . In addition, the $L$ -cospectral graphs with $C_{6} \times K_{m}$ and $Θ_{3, 2, 5} \times K_{m}$ have been found.

19 pages, we showed that several types of graph product are determined by their Laplacian spectra

Laplacian spectral characterization of some graph products

Abstract

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