(β,α)− Connectivity Index of Graphs

• Autores: B. Basavanagoud, Viena R. Desai, Shreekant Patil
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 2, Nº. 1, 2017, págs. 21-30
• Idioma: español
• DOI: 10.21042/amns.2017.1.00003
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• Resumen

  • Let Eβ(G) be the set of paths of length β in a graph G. For an integer β≥1 and a real number α, the (β,α)-connectivity index is defined as βχα(G)=∑v1v2⋅⋅⋅vβ+1∈Eβ(G)(dG(v1)dG(v2)...dG(vβ+1))α. The (2,1)-connectivity index shows good correlation with acentric factor of an octane isomers. In this paper, we compute the (2,α)-connectivity index of certain class of graphs, present the upper and lower bounds for (2,α)-connectivity index in terms of number of vertices, number of edges and minimum vertex degree and determine the extremal graphs which achieve the bounds. Further, we compute the (2,α)-connectivity index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p,q], tadpole graphs, wheel graphs and ladder graphs.