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Domination in generalized unit and unitary Cayley graphs of finite rings

Author

Listed:
  • T. Tamizh Chelvam

    (Manonmaniam Sundaranar University)

  • S. Anukumar Kathirvel

    (Manonmaniam Sundaranar University)

  • M. Balamurugan

    (Manonmaniam Sundaranar University)

Abstract

Let R be a finite commutative ring with nonzero identity and U(R) be the set of all units of R. The graph Γ is the simple undirected graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u in U(R) such that x + uy is a unit in R. Also, $$\overline{\Gamma}$$Γ¯ denotes the complement of Γ. In this paper, we find the domination number γ of Γ as well as $$\overline{\Gamma}$$Γ¯ and characterize all γ-sets in Γ and $$\overline{\Gamma}$$Γ¯. Also, we obtain the bondage number of Γ. Further, we obtain the values of some domination parameters like independent, strong and weak domination numbers of $$\overline{\Gamma}$$Γ¯.

Suggested Citation

  • T. Tamizh Chelvam & S. Anukumar Kathirvel & M. Balamurugan, 2020. "Domination in generalized unit and unitary Cayley graphs of finite rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 533-556, June.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:2:d:10.1007_s13226-020-0415-7
    DOI: 10.1007/s13226-020-0415-7
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    References listed on IDEAS

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    1. Liu, Xiaogang & Li, Binlong, 2016. "Distance powers of unitary Cayley graphs," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 272-280.
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