Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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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)
  • Received : 2019.01.29
  • Accepted : 2020.08.05
  • Published : 2020.09.30
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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.

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References

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