Comparing the second multiplicative Zagreb coindex with some graph invariants

Abstract

‎‎The second multiplicative Zagreb coindex of a simple graph $G$ is‎ ‎defined as‎: ‎$${overline{Pi{}}}_2left(Gright)=prod_{uvnotin{}E(G)}d_Gleft(uright)d_Gleft(vright),$$‎ ‎where $d_Gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$G$‎. ‎In this paper‎, ‎we compare $overline{{Pi}}_2$-index with‎ ‎some well-known graph invariants such as the Wiener index‎, ‎Schultz‎ ‎index‎, ‎eccentric connectivity index‎, ‎total eccentricity‎, ‎eccentric-distance sum‎, ‎the first Zagreb index and coindex and the‎ ‎first multiplicative Zagreb index and coindex‎.