On the Spectral Characterizations of Graphs

• Autorzy: Jing Huang , Shuchao Li
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Laplacian spectrum; adjacency spectrum; cospectral graphs; spectral characterization

Kategorie tematyczne

• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 3
• Strony: 729-744

Daty

wydano

2017-08-01

otrzymano

2015-01-02

poprawiono

2016-06-13

zaakceptowano

2016-06-13

online

2017-07-06

Twórcy

autor

Jing Huang

• , , , P.R.

autor

Shuchao Li

• , , , P.R.

Identyfikatory

DOI

10.7151/dmgt.1979