ashwini index of a ‎graph‎

Motivated by the terminal wiener index, we define the ashwini index a of trees asa(t) = ?1?i < j?ndt (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 shortestpath 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 theashwini index are obtained for detour saturated trees t3(n), t4(n) as well as a class of dendrimersdh.