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Matching Number, Independence Number, and Covering Vertex Number of Γ( Z n )

Author

Listed:
  • Eman AbuHijleh

    (Department of Basic Sciences, Al-Balqa Applied University, Al-Zarka 13110, Jordan)

  • Mohammad Abudayah

    (School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan)

  • Omar Alomari

    (School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan)

  • Hasan Al-Ezeh

    (Department of Mathematics, The University of Jordan, Amman 11942, Jordan)

Abstract

Graph invariants are the properties of graphs that do not change under graph isomorphisms, the independent set decision problem, vertex covering problem, and matching number problem are known to be NP-Hard, and hence it is not believed that there are efficient algorithms for solving them. In this paper, the graph invariants matching number, vertex covering number, and independence number for the zero-divisor graph over the rings Z p k and Z p k q r are determined in terms of the sets S p i and S p i q j respectively. Accordingly, a formula in terms of p , q , k , and r , with n = p k , n = p k q r is provided.

Suggested Citation

  • Eman AbuHijleh & Mohammad Abudayah & Omar Alomari & Hasan Al-Ezeh, 2019. "Matching Number, Independence Number, and Covering Vertex Number of Γ( Z n )," Mathematics, MDPI, vol. 7(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:49-:d:195280
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