Korean J. Math. Vol. 28 No. 3 (2020) pp.405-419
DOI: https://doi.org/10.11568/kjm.2020.28.3.405

The zeroth-order general Randic index of graphs with a given clique number

Main Article Content

Jianwei Du
Yanling Shao
Xiaoling Sun

Abstract

The zeroth-order general Randi\'{c} index $^{0}R_{\alpha}(G)$ of the graph $G$ is defined as $\sum_{u\in V(G)}d(u)^{\alpha}$, where $d(u)$ is the degree of vertex $u$ and $\alpha$ is an arbitrary real number. In this paper, the maximum value of zeroth-order general Randi\'{c} index on the graphs of order $n$ with a given clique number is presented for any $\alpha\neq 0,1$ and $\alpha \notin (2,2n-1]$, where $n=|V(G)|$. The minimum value of zeroth-order general Randi\'{c} index on the graphs with a given clique number is also obtained for any $\alpha\neq 0,1$. Furthermore, the corresponding extremal graphs are characterized.



Article Details

Supporting Agencies

Shanxi Province Science Foundation for Youths [grant number 201901D211227]

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