# Reformulated F-index of graph operations

Document Type : Original paper

Authors

1 Department of Mathematics Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran

2 Department of Mathematics and Computer Science, Sirjan University of Technology Sirjan, I.R. Iran

Abstract

The first general Zagreb index is defined as $M_1^\lambda(G)=\sum_{v\in V(G)}d_{G}(v)^\lambda$ where $\lambda\in \mathbb{R}-\{0,1\}$. The case $\lambda=3$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as $EM_1^\lambda(G)=\sum_{e\in E(G)}d_{G}(e)^\lambda$ and the reformulated F-index is  $RF(G)=\sum_{e\in E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated F-index for some graph operations.

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