Steiner distance in chemical graph theory

Abstract

Steiner distance dG(S) is a natural generalization of the concept of distance in a graph. For a connected graph G of order at least 2 and S ⊆ V (G), dG(S) is equal to the minimum size among all connected subgraphs whose vertex sets are equal to the set S. Here, the known results on the Steiner distance parameters used in chemical graph theory such as Steiner Wiener index, Steiner degree distance, Steiner Harary index, Steiner Gutman index, Steiner hyper–Wiener index, and Steiner Hosoya polynomial are surveyed. Additionally, some conjectures and open problems are listed.