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A simple approach to order the multiplicative Zagreb indices of connected graphs | ||
| Transactions on Combinatorics | ||
| مقاله 3، دوره 1، شماره 4، اسفند 2012، صفحه 17-24 اصل مقاله (448.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2012.2146 | ||
| نویسنده | ||
| Mehdi Eliasi* | ||
| Department of Mathematics and Computer Science , Faculty of Khansar, Khansar, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| multiplicative Zagreb index؛ Majorization؛ Unicyclic graphs؛ bicyclic graphs | ||
| مراجع | ||
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