Drs. Kelly J. Pearson and Tan Zhang are our featured authors this week from the Mathematics and Statistics department at Murray State University. The authors recently published an article titled, “The Laplacian tensor of a multi-hypergraph,” in volume 338, issue 6, of Discrete Mathematics. This article will likely be of interest to those interested in mathematics and physics.
We define a new hyper-adjacency tensor A(H) and use it to define the Laplacian L(H) and the signless Laplacian Q(H) of a given uniform multi-hypergraph H. We prove L(H)) and Q(H) are positive semi-definite (PSD) for connected even uniform multigraphs. Some analyses on the largest and smallest H and Z-eigenvalues of L(H) are given as well as a comparison of other adjacency tensors. (C) 2015 Elsevier B.V. All rights reserved.