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 In1972. 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) = ∑_veVd_v² and Second Zagreb index Zg₂(G) =∑_e=uveE(G)(d_u·d_v) of G and H, as well as First Zagreb polynomial Zg₁(G,x ) =∑_e=uveE(G)x^d_u+d_v and Second Zagreb Polynomial Zg₂(G,x) = ∑_e=uveE(G)x^d_u·d_v