on trees and the multiplicative sum zagreb index
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abstract
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 decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb indeces among all trees of order $ngeq 13$.
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Journal title:
communication in combinatorics and optimizationجلد ۱، شماره ۲، صفحات ۱۳۷-۱۴۸
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