Laplacian integrality in P4-sparse and P4-extendible graphs
Discrete Mathematics
2016-11-28 v1 Combinatorics
Abstract
Let G be a simple graph and L = L(G) the Laplacian matrix of G. G is called L-integral if all its Laplacian eigenvalues are integer numbers. It is known that every cograph, a graph free of P4, is L-integral. The class of P4-sparse graphs and the class of P4-extendible graphs contain the cographs. It seems natural to investigate if the graphs in these classes are still L-integral. In this paper we characterized the L-integral graphs for both cases, P4-sparse graphs and P4-extendible graphs.
Cite
@article{arxiv.1611.08271,
title = {Laplacian integrality in P4-sparse and P4-extendible graphs},
author = {Renata Del-Vecchio and Atila Jones},
journal= {arXiv preprint arXiv:1611.08271},
year = {2016}
}
Comments
10 pages, 6 figures