2014/03/19 by Jia‐Yu Shao, Jia-Yu Shao, Haiying Shan +6
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Tensor decomposition and applications #math.CO
paper · pdf · doi:10.48550/arxiv.1403.4845
16 pages
arxiv created 2014/03/19 · openalex publication_date 2014/03/19 · arxiv updated 2014/03/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
A k-uniform hypergraph G=(V,E) is called odd-bipartite ([5]), if k is even and there exists some proper subset V1 of V such that each edge of G contains odd number of vertices in V1. Odd-bipartite hypergraphs are generalizations of the ordinary bipartite graphs. We study the spectral properties of the connected odd-bipartite hypergraphs. We prove that the Laplacian H-spectrum and signless Laplacian H-spectrum of a connected k-uniform hypergraph G are equal if and only if k is even and G is odd-bipartite. We further give several spectral characterizations of the connected odd-bipartite hypergraphs. We also give a characterization for a connected k-uniform hypergraph whose Laplacian spectral radius and signless Laplacian spectral radius are equal, thus provide an answer to a question raised in [9]. By showing that the Cartesian product G\Box H of two odd-bipartite k-uniform hypergraphs is still odd-bipartite, we determine that the Laplacian spectral radius of G\Box H is the sum of the Laplacian spectral radii of G and H, when G and H are both connected odd-bipartite.