Eigenvalue bounds for the signless p-Laplacian

2016/10/05 by Borba, Elizandro Max, Schwerdtfeger, Uwe
#05C40 #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.01357

Abstract

We consider the signless p-Laplacian of a graph, a generalisation of the usual signless Laplacian (the case p=2). We show a Perron-Frobenius property and basic inequalites for the largest eigenvalue and provide upper and lower bounds for the smallest eigenvalue in terms of a parameter related to the bipartiteness. The latter result generalises bounds by Desai and Rao and, interestingly, in the limit p→ 1 upper and lower bounds coincide.

Related

• A lower bound of the least signless Laplacian eigenvalue of a graph
• Bounding the sum of the largest signless Laplacian eigenvalues of a graph
• On the Main Signless Laplacian Eigenvalues of a Graph
• Notes on the sum of powers of the signless Laplacian eigenvalues of graphs
• Distribution of signless Laplacian eigenvalues and graph invariants