University of IsfahanTransactions on Combinatorics2251-86575120160301Ordering of trees by multiplicative second Zagreb index4955995610.22108/toc.2016.9956ENMehdi EliasiDepartment of Mathematics and Computer Science , Faculty of Khansar, Khansar, IranAli GhalavandDepartment of
Mathematics and Computer Science, Faculty of Khansar, University
of Isfahan, P.O.Box 87931133111, Khansar, IranJournal Article20150608For a graph $G$ with edge set $E(G)$, the multiplicative second Zagreb index of $G$ is defined as $Pi_2(G)=Pi_{uvin E(G)}[d_G(u)d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$. <br />In this paper, we identify the eighth class of trees, with the first through eighth smallest multiplicative second Zagreb indeces among all trees of order $ngeq 14$. <br /> http://toc.ui.ac.ir/article_9956_8efd28a3432a71695fc6a83d711c626e.pdf