Partial characterization of graphs having a single large Laplacian eigenvalue
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Date
2018Author
Type
Abstract
The parameter (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 (G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between (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 cographs, forest ...
The parameter (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 (G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between (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 cographs, forests, and split graphs. ...
In
The Electronic Journal of Combinatorics. United States. Vol. 25, n. 4, 2018, p. 1-10, P4.65
Source
Foreign
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