Using the Cut Method to Computing Edge Version of Co-PI Index of Circumcoronene Series of Benzenoid H_k

摘要

Let G=(V,E) be a simple finite molecular graph in, chemical graph theory. The chemical graph theory is an important branch of mathematical chemistry and computations of the molecular descriptors present very useful properties of chemical molecules. The Wiener index W(G) is the oldest topological indices, (based structure descriptors) and defined as W(G) = (1/2)∑_(v∈V(G))∑_(u∈V(G)~(d(v,u))) One of the important topological indices is Padmakar- Ivan index that introduced by Khadikar and co-authors in 2000. PI_e(G)and PI_v(G)are equal to PI_e=∑_(e∈E(G))(m_u (e|G)+m_v(e|G)) and PI_V = ∑_(e∈E(G))(n_u(e |G)+n_ v(e|G)), respectively. In which m_u(e|G) is the number of edges of G lying closer to u than to v and n_u(e|G) is the number of vertices of G lying closer to u than to v. Recently, Iranmanesh et al. introduced the new index similar to the vertex version of PI index, which isCo-PI_v (G) = ∑_(e∈E(G))|n_u(e|G)-n_v(e|G|). In this paper, we define a new version of PI_e(G) and introduce a closed formula of this new index of Circumcoronene Series of Benzenoid H_k, by using the Cut Method.