A note on the minimum reduced reciprocal Randi\'c index of n-vertex unicyclic graphs

TL;DR

This paper identifies the unicyclic graph with a fixed number of vertices that has the smallest reduced reciprocal Randić index, contributing to the understanding of extremal properties in graph theory.

Contribution

It characterizes the unicyclic graph with the minimum reduced reciprocal Randić index among all graphs with a given number of vertices.

Findings

Identifies the extremal unicyclic graph with minimum index

Provides a characterization theorem for such graphs

Enhances understanding of index behavior in unicyclic graphs

Abstract

The graph having the minimum reduced reciprocal Randi\'c index is characterized among the class of all unicyclic graphs with fixed number of vertices.