en تخصصي Special پژوهشي Research paper <div style="text-align: justify;"><span class="fontstyle0">The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity coindex of some graph products such as lexicographic product, generalized hierarchical product, and strong product. Results are applied to compute the values of this eccentricity-based invariant for some chemical graphs and nanostructures such as hexagonal chain, linear phenylene chain, and zig-zag polyhex nanotube.</span></div> Eccentricity of a vertex, Graph invariants, Graph products, Chemical graphs. 165 178 http://ijmsi.ir/browse.php?a_code=A-10-702-1&slc_lang=en&sid=1 Mahdieh Azari mahdie.azari@gmail.com 100319475328460010028 100319475328460010028 Yes Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran