University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 2 2021 06 01 On Eccentricity Version of Zagreb Coindices 107 120 111483 10.22052/mir.2021.240325.1247 EN Mahdieh Azari Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran Journal Article 2020 10 18 The eccentric connectivity coindex has recently been introduced (Hua and Miao, 2019) as the total eccentricity sum of all pairs of non-adjacent vertices in a graph. Considering the total eccentricity product of non-adjacent vertex pairs, we introduce here another invariant of connected graphs called the second Zagreb eccentricity coindex. We study some mathematical properties of the eccentric connectivity coindex and second Zagreb eccentricity coindex. We also determine the extremal values of the second Zagreb eccentricity coindex over some specific families of graphs such as trees, unicyclic graphs, connected graphs, and connected bipartite graphs and describe the extremal graphs. Moreover, we compare the second Zagreb eccentricity coindex with the eccentric connectivity coindex and give directions for further studies. https://mir.kashanu.ac.ir/article_111483_52ce0302c93b88ca34e84821eda30f35.pdf