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Spectra of extended double cover graphs

Zhibo Chen (2004)

Czechoslovak Mathematical Journal

The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph G with vertex set V = { v 1 , v 2 , ⋯ , v n } , the extended double cover of G , denoted G * , is the bipartite graph with bipartition ( X , Y ) where X = { x 1 , x 2 , ⋯ , x n } and Y = { y 1 , y 2 , ⋯ , y n } , in which x i and y j are adjacent iff i = j or v i and v j are adjacent in G . In this paper we obtain formulas for the characteristic polynomial and the spectrum of G * in terms of the corresponding information of G . Three formulas are derived for the number of spanning trees in G * for a connected...

Spectral characterization of multicone graphs

Jianfeng Wang, Haixing Zhao, Qiongxiang Huang (2012)

Czechoslovak Mathematical Journal

A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho's result [B. Zhou, H. H. Cho, Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 (130) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph. Additionally,...

Spectral integral variation of trees

Yi Wang, Yi-Zheng Fan (2006)

Discussiones Mathematicae Graph Theory

In this paper, we determine all trees with the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing respectively by 1 and the other Laplacian eigenvalues remaining fixed. We also investigate a situation in which the algebraic connectivity is one of the changed eigenvalues.

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L 2 X , μ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula.

Spectral radius and Hamiltonicity of graphs with large minimum degree

Vladimir Nikiforov (2016)

Czechoslovak Mathematical Journal

Let G be a graph of order n and λ ( G ) the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G . One of the main results of the paper is the following theorem: Let k ≥ 2 , n ≥ k ...

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