Comparing the second multiplicative Zagreb coindex with some graph invariants

Document Type : Research Paper


1 Science and Research Branch, Islamic Azad University

2 Department of Mathematics, Tarbiat Modares University, P. O. Box 14115-137, Tehran

3 Kazerun Branch, Islamic Azad University


‎‎The second multiplicative Zagreb coindex of a simple graph $G$ is‎ ‎defined as‎: ‎$${\overline{\Pi{}}}_2\left(G\right)=\prod_{uv\not\in{}E(G)}d_G\left(u\right)d_G\left(v\right),$$‎ ‎where $d_G\left(u\right)$ 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.


Main Subjects

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