Open AccessLaplacian integral graphs with a given degree sequence constraint
Author(s) -
Anderson Fernandes Novanta,
Carla Oliveira,
Leonardo de Lima
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4735
Subject(s) - combinatorics , mathematics , adjacency matrix , laplacian matrix , bipartite graph , degree matrix , vertex (graph theory) , diagonal matrix , eigenvalues and eigenvectors , degree (music) , discrete mathematics , graph power , graph , diagonal , line graph , physics , geometry , quantum mechanics , acoustics
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 if all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all Lintegral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three.