Remark on upper bounds of Randiç index of a graph

Milanoviç, I. Ž., Bekakos, P. M, Bekakos, M. P. and Milanoviç, E. I.

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creative_2016_25_1_71_75

Issue no: Vol 25/2016 no. 1 Tags: upper bounds, General Randi´c index, vertex degree

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Let $G=(V, E)$ be an undirected simple graph of order $n$ with $m$ edges without isolated vertices. Further, let $d_1\ge d_2\ge \cdots \ge d_n$ be vertex degree sequence of $G$ . General Randi\’ c index of graph $G=(V,E)$ is defined by $\displaystyle R_{\alpha}=\sum_{(i,j)\in E}(d_id_j)^{\alpha}$ , where $\alpha \in \mathbb{R} -\{0\}$ . We consider the case when $\alpha =-1$ and obtain upper bound for $R_{-1}$ .