IJPAM: Volume 106, No. 1 (2016)

ECCENTRIC CONNECTIVITY INDEX OF
SOME CHEMICAL TREES

R.S. Haoer$^1$, K.A. Atan$^2$, A.M. Khalaf$^3$, M. Rushdan$^4$, R. Hasni$^5$
$^{1,3}$Department of Mathematics
Faculty of Computer Science and Mathematics
University of Kufa
Najaf, IRAQ
$^{1,2,4}$Institute for Mathematical Research
Universiti Putra Malaysia
43400 Serdang, Selangor, MALAYSIA
$^5$Department of Mathematics
Faculty of Science and Technology
University Malaysia Terengganu
21030 UMT Terengganu, MALAYSIA


Abstract. Let $G = (V, E)$ be a simple connected molecular graph. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by $ V(G)$ and $E(G)$, respectively. If $d(u, v)$ be the notation of distance between vertices $\ u,v \in V(G)$ and is defined as the length of a shortest path connecting them.Then, the eccentricity connectivity index of a molecular graph $G$ is defined as $\xi (G)=\sum_{v\in V(G)}deg(v) ec(v)$, where $deg(v)$ is degree of a vertex $\ v \in V(G)$, and is defined as the number of adjacent vertices with $v$. $ec(v)$ is eccentricity of a vertex $\ v \in V(G)$ , and is defined as the length of a maximal path connecting to another vertex of $v$. In this paper, we establish the general formulas for the eccentricity connectivity index of some classes of chemical trees.

Received: September 18, 2015

AMS Subject Classification: 92E10

Key Words and Phrases: eccentric connectivity index, eccentricity, chemical trees

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DOI: 10.12732/ijpam.v106i1.12 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 157 - 170


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