On the degeneracy of the orbit polynomial and related graph polynomials

Abstract

<p>The orbit polynomial is a new graph counting polynomial which is defined as (formula presented) where O<sub>1</sub>, …, O<sub>r</sub> 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.</p>