The First Eccentric Zagreb Index of Linear Polycene Parallelogram of Benzenoid

作     者：Mehdi Alaeiyan Mohammad Reza Farahani Muhammad Kamran Jamil M. R. Rajesh Kanna Mehdi Alaeiyan;Mohammad Reza Farahani;Muhammad Kamran Jamil;M. R. Rajesh Kanna

作者机构：Department of Mathematics of Iran University of Science and Technology (IUST) Tehran Iran Department of Mathematics Riphah Institute of Computing and Applied Sciences (RICAS) Riphah International University Lahore Pakistan Department of Mathematics Maharani’s Science College for Women Mysore India 

出 版 物：《Open Journal of Applied Sciences》 (应用科学（英文）)

年 卷 期：2016年第6卷第5期

页      面：315-318页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Molecular Graph Linear Polycene Parallelogram of Benzenoid Zagreb Topological Index Eccentricity Connectivity Index Cut Method 

摘      要：Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as Σuv∈E(G)x(du+dv) and Σe=uv∈E(G)(du+dv) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg1*=Σuv∈E(G)(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.