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On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs.
- Source :
-
Linear Algebra & its Applications . Sep2015, Vol. 480, p93-106. 14p. - Publication Year :
- 2015
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SET theory
*BIPARTITE graphs
*UNIFORM algebras
*HYPERGRAPHS
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 480
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 102786697
- Full Text :
- https://doi.org/10.1016/j.laa.2015.04.005