## Abstract

Let *E _{β}* (

*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

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 *TUC*
_{4}
*C*
_{8}[*p,q*], tadpole graphs, wheel graphs and ladder graphs.