Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues

Shenglong Hu, Liqun Qi, Jia Yu Shao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

72 Citations (Scopus)

Abstract

In this paper, we introduce the class of cored hypergraphs and power hypergraphs, and investigate the properties of their Laplacian H-eigenvalues. From an ordinary graph, one may generate a k-uniform hypergraph, called the kth power hypergraph of that graph. Power hypergraphs are cored hypergraphs, but not vice versa. Sunflowers, loose paths and loose cycles are power hypergraphs, while squids, generalized loose s-paths and loose s-cycles for 2≤s<k/2 are cored hypergraphs, but not power graphs in general. We show that the largest Laplacian H-eigenvalue of an even-uniform cored hypergraph is equal to its largest signless Laplacian H-eigenvalue. Especially, we find out these largest H-eigenvalues for even-uniform squids. Moreover, we show that the largest Laplacian H-eigenvalue of an odd-uniform squid, loose path and loose cycle is equal to the maximum degree, i.e., 2. We also compute the Laplacian H-spectra of the class of sunflowers. When k is odd, the Laplacian H-spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well.
Original languageEnglish
Pages (from-to)2980-2998
Number of pages19
JournalLinear Algebra and Its Applications
Volume439
Issue number10
DOIs
Publication statusPublished - 15 Nov 2013

Keywords

  • H-eigenvalue
  • Hypergraph
  • Laplacian
  • Power hypergraph
  • Tensor

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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