Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871383 | Discrete Applied Mathematics | 2018 | 5 Pages |
Abstract
Given a simple undirected graph G=(V,E) with n vertices, if for the largest eigenvalue of its Laplacian matrix λ1 there exists a lower bound λ1â¥Î±â¥dGnnâ1, then we have that its Laplacian energy satisfies LE(G)â¥max{2dG,2(αâdG)},where dG=d1+â¯dnn is the average degree of G. This generic lower bound, obtained with the majorization technique, allows us to obtain two lower bounds for LE(G) which are valid for any connected bipartite graph, and for which the equalities are attained by Kn2,n2 and Sn.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
José Luis Palacios,