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 k-set and each edge into a (k − 2s)-set, where2 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 nonodd-bipartite hypergraphs G k, k 2 . In addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors.

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