This volume continues a series of monographs in algebraic graph theory that specialize to spectral graph theory — the study of interconnections between the properties of a graph and the eigen-values and eigenvectors of the associated adja-cency matrix. The common thread between the two previous works, Spectra of Graphs — Theory and Applications [3] and Recent Results in the Theory of Graph Spec...

The Dilworth number of a graph is the size of the largest subset of its nodes in which the close neighborhood of no node contains the neighborhood of another one. In this paper we give a new characterization of Dilworth k graphs, for each value of k, exactly defining their structure. Moreover, we put these graphs in relation with pairwise compatibility graphs (PCGs), i.e. graphs on n nodes that...

The adjacency spectrum of a graph Γ , which is denoted by Spec(Γ ), is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ ′ are cospectral if Spec(Γ ) = Spec(Γ ). In this paper for each prime number p, p ≥ 23, we construct a large family of cospectral non-isomorphic Cayley graphs over the dihedral group of order 2p. © 2016 Elsevier B.V. All rights reserved.

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.

A multigraph is exactly k-edge-connected if there are exactly k edgedisjoint paths between any pair of vertices. We characterize the class of exactly 3-edge-connected graphs, giving a synthesis involving two operations by which every exactly 3-edge-connected multigraph can be generated. Slightly modi ed syntheses give the planar exactly 3-edge-connected graphs and the exactly 3-edge-connected g...

It is conjectured that connected graphs with given number of vertices and minimum spectral gap (i.e., the difference between their two largest eigenvalues) are double kite graphs. The conjecture is confirmed for connected graphs with at most 10 vertices, and, using variable neighbourhood metaheuristic, there is evidence that it is true for graphs with at most 15 vertices. Several spectral prope...