%0 Journal Article
%T On trees and the multiplicative sum Zagreb index
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Eliasi, Mehdi
%A Ghalavand, Ali
%D 2016
%\ 12/01/2016
%V 1
%N 2
%P 137-148
%! On trees and the multiplicative sum Zagreb index
%K Multiplicative Sum Zagreb Index
%K Graph Transformation
%K Branching Point
%K trees
%R 10.22049/cco.2016.13574
%X For 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 $ngeq 13$.
%U http://comb-opt.azaruniv.ac.ir/article_13574_13979e274d477e710da9e35a059bc605.pdf