On the Stress-sum Index of the Middle and Central Graph of a Graph

Abstract

Ranking molecular chemical compounds or large networks is a complex
task due to their inherent degeneracy. Centrality measures helps to
estimate the rank of each molecular chemical graph. One such centrality
measure is the stress centrality, which quantifies the number of shortest
paths passing through a given vertex. Recently, new topological indices
based on stress have been introduced. In this study, we derive bounds
and exact expressions for the stress of a vertex in the middle and central
graphs derived from a given graph. Additionally, we present expressions
for the stress and stress-sum index of both the middle and central graphs
of a few standard graphs.