Laplacian integral graphs with a given degree sequence constraint
Combinatorics
2020-09-28 v1 Spectral Theory
Abstract
Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) - A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be L-integral is all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all L-integral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three.
Cite
@article{arxiv.2009.11985,
title = {Laplacian integral graphs with a given degree sequence constraint},
author = {Anderson Fernandes Novanta and Carla S. Oliveira and Leonardo S. de Lima},
journal= {arXiv preprint arXiv:2009.11985},
year = {2020}
}
Comments
17 pages