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arXiv · 1711.09014

The multiplicative Zagreb indices of graphs with given connectivity or number of pendant vertices

Shengjin Ji·Shaohui Wang·Tilahun Muche·Sakander Hayat
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Abstract

For a graph $G$, the first multiplicative Zagreb index $\prod_1(G) $ is the product of squares of vertex degrees, and the second multiplicative Zagreb index $\prod_2(G) $ is the product of products of degrees of pairs of adjacent vertices. In this paper, we explore graphs with extremal $\Pi_{1}(G)$ and $\Pi_{2}(G)$ in terms of (edge) connectivity and pendant vertices. The corresponding extremal graphs are characterized with given connectivity at most $k$ and $p$ pendant vertices. In addition, the maximum and minimum values of $\prod_1(G) $ and $\prod_2(G) $ are provided. Our results extend and enrich some known conclusions.

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Shengjin Ji, Shaohui Wang, Tilahun Muche, Sakander Hayat. 2017-11-24. The multiplicative Zagreb indices of graphs with given connectivity or number of pendant vertices. https://arxiv.org/abs/1711.09014

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