Resumen de (β,α)− Connectivity Index of Graphs

B. Basavanagoud, Viena R. Desai, Shreekant Patil

• 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.