Ordering of trees by multiplicative second Zagreb index

Document Type: Research Paper

Authors

1 Department of Mathematics and Computer Science , Faculty of Khansar, Khansar, Iran

2 Department of Mathematics and Computer Science, Faculty of Khansar, University of Isfahan, P.O.Box 87931133111, Khansar, Iran

Abstract

‎For a graph $G$ with edge set $E(G)$‎, ‎the multiplicative second Zagreb index of $G$ is defined as‎ ‎$\Pi_2(G)=\Pi_{uv\in E(G)}[d_G(u)d_G(v)]$‎, ‎where $d_G(v)$ is the degree of vertex $v$ in $G$‎.
‎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 $n\geq 14$‎.
 

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