On the steiner (revised) szeged index

The kth Steiner (revised) Szeged index is defined from Steiner distance, in order to generalize the (revised) Szeged index. In this paper, we obtain some upper and lower bounds on the kth Steiner (revised) Szeged index of graphs. Then we give Nordhaus-Gaddum-type results of the kth Steiner (revised) Szeged index of graphs. Moreover, we determine a formula on rSz_k(G) for trees in general, and present a lower bound on the third Steiner Szeged index for trees of order n and characterize the graphs which attained the bound. Finally, we prove that the path P_n gives the maximum value of the third Steiner Szeged index among the star-like trees of order n ≥ 10.