Multiplicative Zagreb indices of cacti

TL;DR

This paper investigates the bounds of the multiplicative Zagreb index in cactus graphs, characterizing extremal graphs and providing new insights into their structural properties relevant to chemistry and graph theory.

Contribution

It introduces a new method to determine upper and lower bounds of the multiplicative Zagreb index for all cactus graphs and characterizes the extremal cases.

Findings

Established bounds for the multiplicative Zagreb index in cactus graphs.

Characterized extremal cactus graphs achieving these bounds.

Provided a new analytical tool for graph index analysis.

Abstract

Let $\prod(G)$ be Multiplicative Zagreb index of a graph G. A connected graph is a cactus graph if and only if any two of its cycles have at most one vertex in common, which has been the interest of researchers in the filed of material chemistry and graph theory. In this paper, we use a new tool to the obtain upper and lower bounds of $\prod(G)$ for all cactus graphs and characterize the corresponding extremal graphs.