Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues

In this paper, we introduce the class of cored hypergraphs and power hypergraphs, and investigate the properties of their Laplacian H-eigenvalues. From an ordinary graph, one may generate a k-uniform hypergraph, called the kth power hypergraph of that graph. Power hypergraphs are cored hypergraphs, but not vice versa. Sunflowers, loose paths and loose cycles are power hypergraphs, while squids, generalized loose s-paths and loose s  -cycles for 2⩽s