The reformulated Zagreb indices of tricyclic graphs

Abstract

Milic˘evic´ et al. first introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. As we know, the Zagreb indices have been found applications in QSPR and QSAR studies. In the paper, we characterize the extremal properties of the first reformulated Zagreb index. We show some graph operations which increase or decrease this index. Furthermore, we determine the sharp bound of the first reformulated Zagreb index among all the extremal tricyclic graphs by these graph operations.