Laplacian and signless Laplacian Z-eigenvalues of uniform hypergraphs

Abstract

We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest (signless) Laplacian Z-eigenvalue of a hypergraph. For a k-uniform hyperstar with d edges (2d≥k≥3), we show that its largest (signless) Laplacian Z-eigenvalue is d.

Keywords

Hypergraph eigenvalue / Laplacian tensor / signless Laplacian tensor / Z-eigenvalue

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Higher Education Press and Springer-Verlag Berlin Heidelberg