Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21281220161201On trees and the multiplicative sum Zagreb index1371481357410.22049/cco.2016.13574ENMehdiEliasiDept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, Iran,AliGhalavandDept. of Mathematics, Khansar Faculty of Mathematics and Computer Science,
Khansar, IranJournal Article20160928For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as $Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$. In this paper, we first introduce some graph transformations that decrease this index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb indices among all trees of order $ngeq 13$.http://comb-opt.azaruniv.ac.ir/article_13574_13979e274d477e710da9e35a059bc605.pdf