University of KashanMathematics Interdisciplinary Research2538-3639Articles in Press20210628On Eccentricity Version of Zagreb Coindices11148310.22052/mir.2021.240325.1247ENMahdiehAzariDepartment of Mathematics, Kazerun Branch, Islamic Azad University,
P. O. Box: 73135-168, Kazerun, IranJournal Article20201018The 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_326b755b40c76d988da74a414ea60c34.pdf