Harmonic and Zagreb Polynomials and Their Applications on Chemical Nano-Structures

Abstract

The graph ???? consists of an ordered pair (????, ????), where ???? represents a nonempty set of elements called vertices for graph ????, and ???? is a family of unordered pairs that may be free of vertices in graph ???? and is called edges for graph ????. G called a simple graph if has not  loops and without parallel edges, all graphs that used in this paper are simple graph. The degree of a vertex  is number of edges E(G) at that vertex V(G) or V(u) where  and  are denoted for degree of vertex [1] [2].