BEHAVIOR OF BICLIQUE NEIGHBORHOOD POLYNOMIALS: 3D VISUALIZATION

Abstract

Graph polynomials captured the interest of discrete mathematicians in recent years. The idea of graph polynomial is representing a graph structure by a polynomial capturing the number of substructures. The structure-neighborhood polynomial surfaced recently as a bivariate polynomial which clusters the structures with some specified neighborhood properties. In 2016, the balanced biclique polynomial was introduced. Recently, the balanced biclique independent neighborhood polynomials have been investigated for several graphs. In this paper, we investigate the behavior of the 3D plot of cycle graph polynomial representations for varying orders of the structure. Moreover, we investigate the balanced biclique independent neighborhood polynomial of stars and visualize the graph polynomials in 3D.