Nordhaus-Gaddum Type Inequalities for Laplacian and Signless Laplacian Eigenvalues

Nordhaus-Gaddum Type Inequalities for Laplacian and Signless Laplacian Eigenvalues

Let G be a graph with n vertices. We denote the largest signless Laplacian eigenvalue of G by q1(G) and Laplacian eigenvalues of G by μ1(G) > · · · > μn−1(G) > μn(G) = 0. It is a conjecture on Laplacian spread of graphs that μ1(G)−μn−1(G) 6 n − 1 or equivalently μ1(G) + μ1(G) 6 2n − 1. We prove the conjecture for bipartite graphs. Also we show that for any bipartite graph G, μ1(G)μ1(G) 6 n(n − ...

H-eigenvalues of Laplacian and Signless Laplacian Tensors

We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H-eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H-eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H-eigenva...

New Theorems for Signless Laplacian Eigenvalues

AMS Mathematics Subject Classification (2000): 05C50

Majorization bounds for signless Laplacian eigenvalues

Signless Laplacian eigenvalues and circumference of graphs

In this paper, we investigate the relation between the Q -spectrum and the structure of G in terms of the circumference of G. Exploiting this relation, we give a novel necessary condition for a graph to be Hamiltonian by means of its Q -spectrum. We also determine the graphs with exactly one or two Q -eigenvalues greater than or equal to 2 and obtain all minimal forbidden subgraphs and maximal ...