On the Z‐eigenvalues of the signless Laplacian tensor for an even uniform hypergraph

Abstract

SUMMARY We generalize the signless Laplacian matrices for graphs to the signless Laplacian tensors for even uniform hypergraphs and set some fundamental properties for the spectral hypergraph theory based upon the signless Laplacian tensors. In particular, the smallest and the largest Z‐eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are studied, and as an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving these two Z‐eigenvalues are presented. Copyright © 2013 John Wiley & Sons, Ltd.