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Computing Open Locating-Dominating Number of Some Rotationally-Symmetric Graphs

Author

Listed:
  • Hassan Raza

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders in buildings and facilities, and utilizing wireless sensor networks for monitoring environmental processes. The system or structure can be illustrated as a graph in each of these applications. Sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The open locating-dominating set S of a graph G = ( V , E ) is the set of vertices that dominates G , and for any i , j ∈ V(G) N ( i ) ∩ S ≠ N ( j ) ∩ S is satisfied. The set S is called the OLD-set of G . The cardinality of the set S is called open locating-dominating number and denoted by γ o l d ( G ) . In this paper, we computed exact values of the prism and prism-related graphs, and also the exact values of convex polytopes of R n and H n . The upper bound is determined for other classes of convex polytopes. The graphs considered here are well-known from the literature.

Suggested Citation

  • Hassan Raza, 2021. "Computing Open Locating-Dominating Number of Some Rotationally-Symmetric Graphs," Mathematics, MDPI, vol. 9(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1415-:d:577145
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    References listed on IDEAS

    as
    1. Yuezhong Zhang & Suogang Gao, 2020. "On the edge metric dimension of convex polytopes and its related graphs," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 334-350, February.
    2. Raza, Hassan & Hayat, Sakander & Pan, Xiang-Feng, 2018. "On the fault-tolerant metric dimension of convex polytopes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 172-185.
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