On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs.

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]