The Steiner Gutman Index of Trees

The concept of Gutman index Gut (G) of a connected graph G was introduced in 1994.The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance.The Steiner Gutman kindex SGut k (G) introduced by Mao et al. in 2018, is defined by SGut k (G) = SV (G),|S|=k vS dG (v) dG (S) , where dG (S) is the Steiner distance of S and dG (v) is the degree of v in G.In this paper, we obtained the relations between Steiner Gutman k-index and Gutman index, Wiener index and Steiner Wiener k-index of trees with k = 3, 4.