On reformulated zagreb indices with respect to tricyclic graphs

Abstract

The authors Mili$\breve{c}$evi$\acute{c}$ et al. introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. In the paper, we characterize the extremal properties of the first reformulated Zagreb index. We first introduce some graph operations which increase or decrease this index. Furthermore, we will determine the extremal tricyclic graphs with minimum and maximum the first Zagreb index by these graph operations.