Comparing the second multiplicative Zagreb coindex with some graph invariants

The second multiplicative Zagreb coindex of a simple graph G is defined as: bar {{Pi}}_2 (G) =prod_{uv notin E (G)}{d_G (u) d_G (v)} where d_G (u) denotes the degree of the vertex u of G. In this paper، we compare bar {{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.