First and Second Zagreb polynomials of VC5C7[p,q] and HC5C7[p,q]nanotubes

Let G = (V,E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. There exist many topological indices and connectivity indices in graph theory. The First and Second Zagreb indices were first introduced by Gutman and Trinajstić in 1972. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. In this paper, we focus on the structure of ”G=VC5C7 [p,q]” and ”H = HC5C7[p,q]” nanotubes and counting First Zagreb index Zg1(G)= ∑v∈V(G)d2v and Second Zagreb index Zg2(G)= ∑e=uv∈E(G)(dux dv) of G and H, as well as First Zagreb polynomial Zg1(G,x )= ∑e=uv∈E(G)xdu+dv and Second Zagreb polynomial Zg2(G,x) =∑e=uv∈E(G)xduxdv.