On the Degeneracy of the Orbit Polynomial and Related Graph Polynomials

The orbit polynomial is a new graph counting polynomial which is defined as OG(x)=&sum
i=1rx|Oi|, where O1, &hellip
Or are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.