Ashwini Index of a ‎Graph‎

Motivated by the terminal Wiener index, we define the Ashwini index A of trees as A(T) = ? 1?i < j?n d T (vi, vj)[degT (N(ui)) + degT (N(vj))], where dT (vi, vj) is the distance between the vertices vi, vj ? V (T), is equal to the length of the shortest path starting at vi and ending at vj and degT (N(v)) is the cardinality of degT (u), where uv ? E(T). In this paper, trees with minimum and maximum A are characterized and the expressions for the Ashwini index are obtained for detour saturated trees T3(n), T4(n) as well as a class of Dendrimers Dh.