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

#### Abstract

*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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DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.545

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