The stabilizing index and cyclic index of the coalescence and Cartesian product of uniform hypergraphs

Abstract

Let G be connected uniform hypergraph and let A(G) be the adjacency tensor of G. The stabilizing index of G is exactly the number of eigenvectors of A(G) associated with the spectral radius, and the cyclic index of G is exactly the number of eigenvalues of A(G) with modulus equal to the spectral radius. Let G1⊙G2 and G1□G2 be the coalescence and Cartesian product of connected m-uniform hypergraphs G1 and G2 respectively. In this paper, we give explicit formulas for the stabilizing indices and cyclic indices of G1⊙G2 and G1□G2 in terms of those of G1 and G2 or the invariant divisors of their incidence matrices over Zm, respectively.