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The General Connectivity and General Sum-Connectivity Indices of Nanostructures

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Abstract:

Let G be a simple graph with vertex set V(G) and edge set E(G). For νiV(G), di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

Info:

Periodical:
International Letters of Chemistry, Physics and Astronomy (Volume 44)
Pages:
73-80
Citation:
M. R. Farahani, "The General Connectivity and General Sum-Connectivity Indices of Nanostructures", International Letters of Chemistry, Physics and Astronomy, Vol. 44, pp. 73-80, 2015
Online since:
January 2015
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