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On the Spectral Characterizations of Graphs

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Huang J., Li S.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

729-744

Several matrices can be associated to a graph, such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some informations about the structure of the graph and the question “Which graphs are determined by their spectrum?” is still a difficult problem in spectral graph theory. Let [...] 𝒰p2q ${\cal U}_p^{2q}$ be the set of graphs obtained from Cp by attaching two pendant edges to each of q (q ⩽ p) vertices on Cp, whereas [...] 𝒱p2q ${\cal V}_p^{2q}$ the subset of [...] 𝒰p2q ${\cal U}_p^{2q}$ with odd p and its q vertices of degree 4 being nonadjacent to each other. In this paper, we show that each graph in [...] 𝒰p2q ${\cal U}_p^{2q}$ , p even and its q vertices of degree 4 being consecutive, is determined by its Laplacian spectrum. As well we show that if G is a graph without isolated vertices and adjacency cospectral with the graph in [...] 𝒱pp−1={H} ${\cal V}_p^{p - 1} = \{ H\}$ , then G ≅ H.

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1 Discussiones Mathematicae Graph Theory

1 Huang J.

1 Li S.

1 2017

Wyniki wyszukiwania

On the Spectral Characterizations of Graphs