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Bounds on the Clique and the Independence Number for Certain Classes of Graphs

Author

Listed:
  • Valentin E. Brimkov

    (Mathematics Department, SUNY Buffalo State, Buffalo, NY 14222, USA
    Valentin E. Brimkov is on leave from Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.)

  • Reneta P. Barneva

    (School of Business, State University of New York at Fredonia, Fredonia, NY 14063, USA)

Abstract

In this paper, we study the class of graphs G m , n that have the same degree sequence as two disjoint cliques K m and K n , as well as the class G ¯ m , n of the complements of such graphs. The problems of finding a maximum clique and a maximum independent set are NP-hard on G m , n . Therefore, looking for upper and lower bounds for the clique and independence numbers of such graphs is a challenging task. In this article, we obtain such bounds, as well as other related results. In particular, we consider the class of regular graphs, which are degree-equivalent to arbitrarily many identical cliques, as well as such graphs of bounded degree.

Suggested Citation

  • Valentin E. Brimkov & Reneta P. Barneva, 2024. "Bounds on the Clique and the Independence Number for Certain Classes of Graphs," Mathematics, MDPI, vol. 12(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:170-:d:1313630
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