(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
The Steiner distance for the set S ⊆ V (G) would simply be the number of edges in the minimal subtree connecting them and is denoted as d_G(S). The Steiner-Harary index is SH_k(G), defined as the sum of the reciprocal of the Steiner distance for all subsets with k vertices in G. In this article, we calculate the exact value of SH_k(G) for specific graphs and establish new best possible lower and upper bounds and characterization. Furthermore, we explore the relationship between SH_k(G) and other graph indices based on Steiner distance.