IJPAM: Volume 106, No. 2 (2016)

THE ATOM BOND CONNECTIVITY INDEX OF
CERTAIN GRAPHS

Mohanad A. Mohammed$^1$, 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. The atom bond connectivity (ABC) index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes, which is defined as $ ABC = \sum_{uv\in E(G)}\sqrt\frac{d_{u} + d_{v} - 2}{d_{u}d_{v}} $, we denotes $d_{u}$ the degree of vertex u in G. In this paper, we study the general formula for ABC index of certain graphs and vertex gluing of graphs.

Received: August 25, 2015

AMS Subject Classification: 97K30

Key Words and Phrases: ABC Index, $K_{4}$-homeomorphism, complete bipartite, k-bridge graph and vertex gluing

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DOI: 10.12732/ijpam.v106i2.6 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: 2
Pages: 415 - 427


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