The edge version of MEC index of one-pentagonal carbon nanocones
Amin Nejati, Mohammadhadi Alaeiyan · 2014
Molecular descriptors are playing significant role in chemistry, pharmacology, etc. Among them, topological indices have a prominent place [15]. There are numerous topological descriptors that have found some applications in theoretical chemistry, especially in QSPR/QSAR research. More recently, a new topological index, eccentric connectivity index, has been investigated. This topological model has been shown to give a high degree of predictability of pharmaceutical properties, and may provide leads for the development of safe and potent anti-HIV compounds. We encourage the reader to consult papers [1–9] for some applications and papers [10– 14] for the mathematical properties of this topological index. One-pentagonal carbon nanocones, Fig. 1, were originally discovered by Ge and Sattler in 1994 [17]. These are constructed from a graphene sheet by removing a 60° wedge and joining the edges thus producing a cone with a single pentagonal defect at the apex. One-pentagonal carbon nanocones consist of one pentagone, its core surrounded by layers of hexagons. If there are n layers, then the graph of this molecule is denoted by G= ] [ CNC5 n . Now, we introduce some notation and terminology. Let G be a graph with vertex set V(G) and edge set E(G). Let deg(v) denote the degree of the vertex v in G. If deg(v) = 1, then v is said to be a pendent vertex. An edge incident to a pendent vertex is said to be a pendent edge. For two vertices u and v in V(G), we denote by d(u,v) the distance between u and v, i.e., the length of the shortest path connecting u and v. The eccentricity of a vertex v in V(G), denoted by ecc(v), is defined as G V u v u d v ecc | , max The diameter of a graph G is then defined to be G V v v ecc | max . The eccentric