F-Index of Four Operations on Graphs

TL;DR

This paper investigates how the F-index, a graph invariant based on vertex degrees, behaves under four specific graph operations, extending the understanding of this index in graph theory.

Contribution

The paper provides new formulas and insights into the F-index for four graph operations, expanding the theoretical framework of degree-based topological indices.

Findings

Derived formulas for F-index under four graph operations

Extended the theoretical understanding of the F-index

Provided tools for future graph analysis

Abstract

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph which was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced. In this paper we study the F-index of four operations on graphs which were introduced by Eliasi and Taeri [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, \textit{Discrete Appl. Math.}\textbf{157}(2009) 794--803.].