On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs
| Autor: | Yi-Zheng Fan, Murad-ul-Islam Khan |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Vertex (graph theory) Numerical Analysis Hypergraph Algebra and Number Theory Simple graph Spectral radius 05C65 15A18 15A69 Blowing up Combinatorics Limit point FOS: Mathematics Bipartite graph Mathematics - Combinatorics Discrete Mathematics and Combinatorics Adjacency list Combinatorics (math.CO) Geometry and Topology Mathematics |
| Zdroj: | Linear Algebra and its Applications. 480:93-106 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2015.04.005 |
| Popis: | In order to investigate the non-odd-bipartiteness of even uniform hypergraphs, starting from a simple graph G, we construct a generalized power of G, denoted by G k , s , which is obtained from G by blowing up each vertex into a s-set and each edge into a ( k − 2 s ) -set, where s ≤ k / 2 . When s k / 2 , G k , s is always odd-bipartite. We show that G k , k 2 is non-odd-bipartite if and only if G is non-bipartite, and find that G k , k 2 has the same adjacency (respectively, signless Laplacian) spectral radius as G. So the results involving the adjacency or signless Laplacian spectral radius of a simple graph G hold for G k , k 2 . In particular, we characterize the unique graph with minimum adjacency or signless Laplacian spectral radius among all non-odd-bipartite hypergraphs G k , k 2 of fixed order, and prove that 2 + 5 is the smallest limit point of the non-odd-bipartite hypergraphs G k , k 2 . In addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors. |
| Databáze: | OpenAIRE |
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