Atom-bond connectivity index of graph with two edges added

Authors

  • Mohamad Nazri Husin School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 UMT Kuala Nerus, Terengganu, Malaysia
  • Roslan Hasni School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 UMT Kuala Nerus, Terengganu, Malaysia

DOI:

https://doi.org/10.11113/matematika.v32.n2.928

Abstract

The atom-bond connectivity index of a graph G, denoted as ABC(G), is defined as the sum of the weight 

sqrt((du+dv-2)/dudv)

of all edges uv of G, where du (or dv) denotes the degree of vertex u (or v) in G. The ABC index provides a good model for the stability of linear and branches alkanes as well as the strain energy of cycloalkanes. In this note, we prove that ABC index of a graph increases when two new edges are added.

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Published

27-04-2017

How to Cite

Husin, M. N., & Hasni, R. (2017). Atom-bond connectivity index of graph with two edges added. MATEMATIKA, 32(2), 81–86. https://doi.org/10.11113/matematika.v32.n2.928

Issue

Volume 32 (December 2016)

Section

Articles

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Copyright of articles that appear in MATEMATIKA: MJIAM belongs exclusively to Penerbit UTM Press, Universiti Teknologi Malaysia. This copyright covers the rights to reproduce the article, including reprints, electronic reproductions or any other reproductions of similar nature.