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Complete solution to a conjecture on Randic index

Author

Listed:
  • Li, Xueliang
  • Liu, Bolian
  • Liu, Jianxi

Abstract

For a graph G, the Randic index R(G) of G is defined by , where d(u) is the degree of a vertex u and the summation runs over all edges uv of G. Let G(k,n) be the set of connected simple graphs of order n with minimum degree k. Bollobás and Erdos once asked for finding the minimum value of the Randic index among the graphs in G(k,n). There have been many partial solutions for this question. In this paper we give a complete solution to the question.

Suggested Citation

  • Li, Xueliang & Liu, Bolian & Liu, Jianxi, 2010. "Complete solution to a conjecture on Randic index," European Journal of Operational Research, Elsevier, vol. 200(1), pages 9-13, January.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:1:p:9-13
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    References listed on IDEAS

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    1. Pavlovic, Ljiljana & Divnic, Tomica, 2007. "A quadratic programming approach to the Randic index," European Journal of Operational Research, Elsevier, vol. 176(1), pages 435-444, January.
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    Cited by:

    1. Mahdi Sohrabi-Haghighat & Mohammadreza Rostami, 2017. "The minimum value of geometric-arithmetic index of graphs with minimum degree 2," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 218-232, July.
    2. Pavlovic, Ljiljana, 2010. "Comment on "Complete solution to a conjecture on Randic index"," European Journal of Operational Research, Elsevier, vol. 207(1), pages 539-542, November.

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