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http://dx.doi.org/10.11568/kjm.2020.28.3.405

THE ZEROTH-ORDER GENERAL RANDIĆ INDEX OF GRAPHS WITH A GIVEN CLIQUE NUMBER  

Du, Jianwei (School of Science, North University of China)
Shao, Yanling (School of Science, North University of China)
Sun, Xiaoling (School of Science, North University of China)
Publication Information
Korean Journal of Mathematics / v.28, no.3, 2020 , pp. 405-419 More about this Journal
Abstract
The zeroth-order general Randić index 0Rα(G) of the graph G is defined as ∑u∈V(G)d(u)α, where d(u) is the degree of vertex u and α is an arbitrary real number. In this paper, the maximum value of zeroth-order general Randić index on the graphs of order n with a given clique number is presented for any α ≠ 0, 1 and α ∉ (2, 2n-1], where n = |V (G)|. The minimum value of zeroth-order general Randić index on the graphs with a given clique number is also obtained for any α ≠ 0, 1. Furthermore, the corresponding extremal graphs are characterized.
Keywords
zeroth-order general $Randi{\acute{c}}$ index; chromatic number; clique number;
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