Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs
TLDR
In this paper, the authors studied the spectral properties of the connected odd-bipartite hypergraphs and showed that the Laplacian H-spectrum and signless H-Spectrum of a connected -uniform hypergraph are equal if and only if the hypergraph is even and is odd.Abstract:
A -uniform hypergraph is called odd-bipartite, if is even and there exists some proper subset of such that each edge of contains odd number of vertices in . 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 -uniform hypergraph are equal if and only if is even and is odd-bipartite. We further give several spectral characterizations of the connected odd-bipartite hypergraphs. We also give a characterization for a connected -uniform hypergraph whose Laplacian spectral radius and signless Laplacian spectral radius are equal; thus, provide an answer to a question raised by L. Qi. By showing that the Cartesian product of two odd-bipartite -uniform hypergraphs is still odd-bipartite, we determine that the Laplacian spectral radius of is the sum of the Laplacian spectral radii of and , when and are both connected odd-bipa...read more
Citations
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The extremal spectral radii of $$k$$k-uniform supertrees
Honghai Li,Jia-Yu Shao,Liqun Qi +2 more
TL;DR: It is proved that for all these three kinds of spectral radii of hypergraphs, the hyperstar of the connected and acyclic supertree attains uniquely the maximum spectral radius among all k-uniform supertrees on n vertices.
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On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs
Murad-ul-Islam Khan,Yi-Zheng Fan +1 more
TL;DR: In this paper, the adjacency or signless Laplacian spectral radius of a simple graph G is characterized for all non-odd-bipartite hypergraphs G k, k 2 of fixed order.
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Some spectral properties of uniform hypergraphs
TL;DR: Some spectral characterizations of odd-bipartite hypergraphs are given, and a partial answer to a question posed by Shao et al (2014) is given.
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The maximum spectral radii of uniform supertrees with given degree sequences
TL;DR: This paper determines the unique k -uniform supertree with the maximum spectral radius among all k - uniform supertrees with a given degree sequence by using 2-switch operation and edge-moving operation on superTrees.
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