Korean Journal of Mathematics

  • 제27권3호
  • /
  • Pages.563-580
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  • 2019
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ON STRONG METRIC DIMENSION OF ZERO-DIVISOR GRAPHS OF RINGS

  • Bhat, M. Imran (Department of Mathematics University of Kashmir) ;
  • Pirzada, Shariefuddin (Department of Mathematics University of Kashmir)
  • 투고 : 2018.10.01
  • 심사 : 2019.08.07
  • 발행 : 2019.09.30
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초록

In this paper, we study the strong metric dimension of zero-divisor graph ${\Gamma}(R)$ associated to a ring R. This is done by transforming the problem into a more well-known problem of finding the vertex cover number ${\alpha}(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring ${\mathbb{Z}}_n$ of integers modulo n and the ring of Gaussian integers ${\mathbb{Z}}_n$[i] modulo n. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.

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연구 과제 주관 기관 : University Grants Commission

참고문헌

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피인용 문헌

  1. On graphs with same metric and upper dimension vol.13, pp.2, 2021, https://doi.org/10.1142/s1793830921500154
  2. On the Strong Metric Dimension of Annihilator Graphs of Commutative Rings vol.44, pp.4, 2019, https://doi.org/10.1007/s40840-020-01062-y