A k-uniform hypergraph G = (V, E) is called odd-bipartite ([5]), if k is even and there exists some proper subset V 1 of V such that each edge of G contains odd number of vertices in V 1 . 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✷H of two odd-bipartite k-uniform hypergraphs is still odd-bipartite, we determine that the Laplacian spectral radius of G✷H is the sum of the Laplacian spectral radii of G and H, when G and H are both connected odd-bipartite.

No abstract

A supertree is a connected and acyclic hypergraph. We study some uniform supertrees with larger spectral radii. We first define a new type of edge-moving operation on hypergraphs, and study its applications on the comparison of the spectral radii of hypergraphs. By using this new operation on some supertrees together with the general edge-moving operation introduced by Li, Shao and Qi in 2015, and using a result by Zhou et al. in 2014 about the relation between the spectral radii of an ordinary graph and its power hypergraph, we are able to determine the first eight k-uniform supertrees on n vertices with the largest spectral radii.

No abstract

No abstract