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ON CLIQUE-CLIQUE DOMINATION NUMBER AND INVERSE CLIQUE TRANSVERSAL NUMBER OF A GRAPH

S. R. Bhat|R. S. Bhat|S. G. Bhat
μž₯μ „μˆ˜ν•™νšŒ (Jangjeon Mathematical Society)|2024.10|Proceedings of the Jangjeon Mathematical Society(μž₯μ „μˆ˜ν•™νšŒ 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27ꢌ 제4호|pp. 733-742|DOI 10.17777/pjms.2024.27.4.017

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Clique-Clique domination numberHajo’s graphclique degreeminimum clique number
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초둝

Let 𝐾(𝐺) denote set of all cliques of a graph 𝐺. Two cliques 𝑙₁, 𝑙₂ ∈ 𝐾(𝐺) are said to clique dominate each other if there is a vertex common to both 𝑙₁ and 𝑙₂. A set 𝐿 βŠ† 𝐾(𝐺) is said to be a clique-clique dominating set (CCD-set) if every clique in 𝐺 is clique dominated by some clique in 𝐿. The clique-clique dominating set having minimum cardinality is called clique-clique domination number γ𝚌𝚌(𝐺). In this paper, several bounds for the above parameter are obtained. Also bounds on number of cliques in a graph is given in terms of clique numbers.

Abstract

Let 𝐾(𝐺) denote set of all cliques of a graph 𝐺. Two cliques 𝑙₁, 𝑙₂ ∈ 𝐾(𝐺) are said to clique dominate each other if there is a vertex common to both 𝑙₁ and 𝑙₂. A set 𝐿 βŠ† 𝐾(𝐺) is said to be a clique-clique dominating set (CCD-set) if every clique in 𝐺 is clique dominated by some clique in 𝐿. The clique-clique dominating set having minimum cardinality is called clique-clique domination number γ𝚌𝚌(𝐺). In this paper, several bounds for the above parameter are obtained. Also bounds on number of cliques in a graph is given in terms of clique numbers.

μ°Έκ³ λ¬Έν—Œ (15)

  1. C. Berge, "Theory of Graphs and its Applications" (1962), Methuen
  2. S. A. Choudam, "Line-Clique Cover Number of a Graph", Proceedings of INSA, 41(3), pp.289~293 (1975)
  3. E. J. Cockayne, "Towards a Theory of Domination in Graphs", Networks, 7, pp.247~261 (1977)
  4. R. Diestel, "Graph Theory" (2000), Springer Verlag Newyork, Electronic Edition
  5. E. M. Kiunisala, "On Clique Secure Domination in Graphs", Glo. J. of Pur. and App. Math., 12(3), pp.2075~2084 (2016)
  6. T.W. Haynes, "Fundamentals of Domination in Graphs" (1998), Marcel Dekker, Inc
  7. J. Lehel, "Neighbourhood Perfect Graphs", Disc. Math, 61, pp.93~101 (1986)
  8. M. B. Cozzens, "Dominating Cliques in Graphs", Disc. Math, 86(1–3), pp.101~116 (1990)
  9. V. Mohanaselvi, "The Clique Neighbourhood Domination Number in Graphs", Int. J. of Eng. Res. & Tech., 5(4), pp.1~7 (2017)
  10. P. Erdos, "Covering the Cliques of a Graph with Vertices", Disc. Math., 108, pp.279~289 (1992)
  11. A. Sudhakaraiah, "Clique Domination in Interval Graphs", Int. J. of Res. in Elec. and Comp. Eng, 2(3), pp.73~77 (2014)
  12. S. R. S. Bhat, "A Counter Example For Neighbourhood Number Less Than Edge Covering Number of a Graph", IAENG Int. J. of App. Math, 52(2), pp.500~506 (2022)
  13. T. V. Daniel, "Clique Domination in a Graph", App. Math. Sci., 9(116), pp.5749~5755 (2015)
  14. Recent Developments in Theory of Domination in Graphs, "H.B. Walikar", The Mehta Research Institute, ~, pp.MRI Lecture notes, No.1 (1979)
  15. D. B. West, "Introduction to Graph Theory" (1996), Prentice Hall

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