Partial characterization of graphs having a single large Laplacian eigenvalue
Allem, L. Emilio · Cafure, Antonio · Dratman, Ezequiel · Grippo, Luciano N. · Safe, Martín D. · Trevisan, Vilmar
Original · EN
The parameter σ(G) of a graph G stands for the number of Laplacian eigenvalues greater than or equal to the average degree of G. In this work, we address the problem of characterizing those graphs G having σ(G)=1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between σ(G) and the number of anticomponents of G. As a by-product, we present some results which support the conjecture, by restricting our analysis to some classes of graphs.
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