Reformulated F-index of graph operations

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.

Keywords

• First general Zagreb index‎
• ‎reformulated first general Zagreb index‎
• ‎F-index‎
• ‎reformulated F-index.