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

Issue

Volume 32 (December 2016)

Section

Articles

License

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.

How to Cite

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