The H-spectra of a class of generalized power hypergraphs

The generalized power of a simple graph G , denoted by G k , s , is obtained from G by blowing up each vertex into an s -set and each edge into a k -set, where 1 ? s ? k 2 . When s < k 2 , G k , s is always odd-bipartite. It is known that G k , k 2 is non-odd-bipartite if and only if G is non-bipartite, and G k , k 2 has the same adjacency (respectively, signless Laplacian) spectral radius as G . In this paper, we prove that, regardless of multiplicities, the H -spectrum of A ( G k , k 2 ) (respectively, Q ( G k , k 2 ) ) consists of all eigenvalues of the adjacency matrices (respectively, the signless Laplacian matrices) of the connected induced subgraphs (respectively, modified induced subgraphs) of G . As a corollary, G k , k 2 has the same least adjacency (respectively, least signless Laplacian) H -eigenvalue as G . We also discuss the limit points of the least adjacency H -eigenvalues of hypergraphs, and construct a sequence of non-odd-bipartite hypergraphs whose least adjacency H -eigenvalues converge to - 2 + 5 .