Steiner wiener index of graph products

Abstract

© 2016. University of Isfahan. All rights reserved. The Wiener index W (G) of a connected graph G is defined as (Presented formula) where dG (u, v) is the distance between the vertices u and v of G. For S ⊆ V (G), the Steiner distance d (S) of the vertices of S is the minimum size of a connected subgraph of G whose vertex set is S. The k-th Steiner Wiener index SWk (G) of G is defined as (Presented formula). We establish expressions for the k-th Steiner Wiener index on the join, corona, cluster, lexicographical product, and Cartesian product of graphs