A simple approach to order the multiplicative Zagreb indices of connected graphs
نویسندگان
1 Department of Mathematics and Computer Science , Faculty of Khansar, Khansar, Iran
doi
10.22108/toc.2012.2146چکیده
The first ($\Pi_1$) and the second $(\Pi_2$) multiplicative Zagreb indices of a connected graph $G$, with vertex set $V(G)$ and edge set $E(G)$, are defined as $\Pi_1(G) = \prod_{u \in V(G)} {d_u}^2$ and $\Pi_2(G) = \prod_{uv \inE(G)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. In this paper we present a simple approach to order these indices for connected graphs on the same number of vertices. Moreover, as an application of this simple approach, we extend the known ordering of the first and the second multiplicative Zagreb indices for some classes of connected graphs.
