Spectra of expansion graphs.
Spectra of extended double cover graphs
The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph with vertex set , the extended double cover of , denoted , is the bipartite graph with bipartition where and , in which and are adjacent iff or and are adjacent in . In this paper we obtain formulas for the characteristic polynomial and the spectrum of in terms of the corresponding information of . Three formulas are derived for the number of spanning trees in for a connected...
Spectra Of Graphs Formed By Some Unary Operations
Spectra of graphs formed by some unary operations.
Spectra of Regular Polytopes.
Spectra of weighted compound graphs of generalized Bethe trees.
Spectra of weighted rooted graphs having prescribed subgraphs at some levels.
Spectral characterization of multicone graphs
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 characterizations of dumbbell graphs.
Spectral Characterizations of Line Graphs. Variations on the Theme
Spectral deformations of automorphic functions over graphs of groups.
Spectral extrema for graphs: the Zarankiewicz problem.
Spectral graph theory and the inverse eigenvalue problem of a graph.
Spectral integral variation of trees
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
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 and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of and then using the Stieltjes inversion formula.
Spectral radius and Hamiltonicity of graphs with large minimum degree
Let be a graph of order and the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in . One of the main results of the paper is the following theorem: Let
Spectral Recognition of Graphs
Spectral saturation: inverting the spectral Turán theorem.
Spectral study of alliances in graphs
In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.
Spectral Techniques in Complex Networks