Steiner Wiener index of block graphs

TL;DR

This paper introduces methods to compute the Steiner $k$-Wiener index in block graphs, a measure related to the sum of Steiner distances among vertex sets, enhancing understanding of graph connectivity.

Contribution

It presents new simple methods for calculating the Steiner $k$-Wiener index specifically for block graphs.

Findings

Provides explicit calculation methods for Steiner $k$-Wiener index in block graphs.

Enhances computational techniques for Steiner distances in graph theory.

Contributes to the analysis of connectivity measures in block graphs.

Abstract

Let $S$ be a set of vertices of a connected graph $G$. The Steiner distance of $S$ is the minimum size of a connected subgraph of $G$ containing all the vertices of $S$. The Steiner $k$-Wiener index is the sum of all Steiner distances on sets of $k$ vertices of $G$. Different simple methods for calculating the Steiner $k$-Wiener index of block graphs are presented.