H-Eigenvalues of signless Laplacian tensor for an even uniform hypergraph

Abstract

The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smallest and the largest H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are discussed, and their relationships to hypergraph bipartition, minimum degree, and maximum degree are described. As an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving the smallest and the largest H-eigenvalues are presented.

Key words： Signless Laplacian tensor; hypergraph; H-eigenvalue; bipartition; maximum degree; bound; edge cut

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