About Atom Bond Connectivity and Geometric-Arithmetic Indices of Special Chemical Molecular and Nanotubes

Authors

  • Mohammad Reza Farahani Department of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran
  • Mohamad Nazri Husin School of Informatics and Applied Mathematics of University Malaysia Terengganu, 21030 Kuala Lumpur Terengganu
  • Waqas Nazeer Division of Science and Technology, University of Education, Lahore 54000

DOI:

https://doi.org/10.26713/jims.v10i1-2.545

Keywords:

Molecular graph, Nanotubes, geometric-arithmetic (GA) index, atom-bond connectivity (ABC) index

Abstract

Among topological descriptors connectivity indices are very important and they have a prominent role in chemistry. Two useful of them are the geometric-arithmetic (GA) and atom-bond connectivity (ABC) indices and are defined as \(GA(G)=\sum\limits _{uv\in E(G)}\frac{2\sqrt{d_{u} d_{v} } }{d_{u} +d_{v} }\) and \(ABC(G)=\sum\limits _{e=uv\in E(G)}\sqrt{\frac{d_{u} +d_{v} -2}{d_{u} d_{v} } }\), in which \(d_u\) and \(d_v\) are the degrees of the vertices \(u\) and \(v\), respectively. n this paper we compute these connectivity topological indices for a special chemical molecular graph ``$Cas(C)$-$CaR(C)[m,n,p]$ Nanotubes Junction'' are given. The $Cas(C)$-$CaR(C)[m,n,p]$ Nanotubes Junction is a new nano-structure that was defined by M.V. Diudea, on based the new graph operations (Leapfrog Le and Capra Ca) on the cycle graph \(C_n\).

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Published

2018-08-09
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How to Cite

Farahani, M. R., Husin, M. N., & Nazeer, W. (2018). About Atom Bond Connectivity and Geometric-Arithmetic Indices of Special Chemical Molecular and Nanotubes. Journal of Informatics and Mathematical Sciences, 10(1-2), 153–160. https://doi.org/10.26713/jims.v10i1-2.545

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Research Articles