Downhill Zagreb Polynomials of Graphs

Abstract

Abstract

In a number of applied and theoretical environments, graph polynomials and their roots have emerged. To deeply explore counting sequences connected to different graph parameters, graph polynomials have been introduced as generating polynomials. In addition, there has been a great deal of recent interest in graph polynomials. The first, second and forgotten downhill Zagreb indices are defined as and . In this paper, we define and study the first, second and forgotten downhill Zagreb polynomials, we compute the exact values of some standard families of graphs. Finally, the first, second and forgotten Zagreb polynomials for firefly graph, Graphene and honeycomb network are obtained with 3D graphical representation.

AMS Subject Classification: 2010: 05C07, 05C30, 05C76.

Keywords: Zagreb downhill polynomial, Downhill Zagreb indices.