On stabilizing index and cyclic index of certain amalgamated uniform hypergraphs

Abstract

Let G be a connected uniform hypergraph and $A\left(G\right)$ be the adjacency tensor of G. The largest absolute value of the eigenvalues of $A\left(G\right)$ is called the spectral radius of G. The number of eigenvectors of $A\left(G\right)$ associated with the spectral radius is called the stabilizing index of G. The number of eigenvalues of $A\left(G\right)$ with modulus equal to the spectral radius is called the cyclic index of G. In this paper, we consider a class of amalgamated uniform hypergraphs and compute its stabilizing index and cyclic index.