Laplacian spectral characterization of some graph products

Details Laplacian spectral characterization of some graph products Laplacian spectral characterization of some graph products

2010-07-15

arxiv.org/abs/1007.2472v3

Mathematics

Combinatorics

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

Scientific paper

This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: $\mathscr{G}={G : |EG|\leq|VG|+1}$, and characterize all graphs $G\in\mathscr{G}$ such that the products $G\times K_m$ are $L$-DS graphs. The main result of this paper states that, if $G\in\mathscr{G}$, except for $C_{6}$ and $\Theta_{3,2,5}$, 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 $\Theta_{3,2,5}\times K_{m}$ have been found.

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