On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs
By Murad-ul-Islam Khan, Yi-Zheng Fan. 2014
93 citations recorded by the source corpus.
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.
Subfields: Computational Mathematics, Computational Theory and Mathematics, Radiology, Nuclear Medicine and Imaging
View Paper: https://www.semanticscholar.org/paper/562483c12045bfb50285d4ce08e15de80fa4e0a3
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In Computational Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Some upper bounds on the eigenvalues of uniform hypergraphs (2015, background): “(See [7,11].”