Premium
On the Z‐eigenvalues of the signless Laplacian tensor for an even uniform hypergraph
Author(s) -
Xie Jinshan,
Chang An
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1910
Subject(s) - hypergraph , mathematics , eigenvalues and eigenvectors , combinatorics , laplace operator , laplacian matrix , tensor (intrinsic definition) , resistance distance , discrete mathematics , graph , pure mathematics , physics , mathematical analysis , line graph , quantum mechanics , graph power
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.