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<p>In a graph <i>G</i>, a locating-dominating set <i>S</i> is a subset of vertices representing “detectors" which locate an “intruder." Detection devices are placed at a set <i>S</i> of locating dominating vertices in <i>G</i> in order to identify an intruder in the system. Error-detecting locating dominating sets (<i>DET</i>&#xa0;:&#xa0;<i>LD</i>) are a fault-tolerant variant of locating dominating sets in which the system has at most one false negative. In this paper, we found the exact value of error-detecting locating domination number of Mycielskian of some classes of graphs.</p>

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Error-detecting locating domination number of Mycielskian of some classes of graphs

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • A. Fathima,
  • M. R. Chithra

摘要

In a graph G, a locating-dominating set S is a subset of vertices representing “detectors" which locate an “intruder." Detection devices are placed at a set S of locating dominating vertices in G in order to identify an intruder in the system. Error-detecting locating dominating sets (DET : LD) are a fault-tolerant variant of locating dominating sets in which the system has at most one false negative. In this paper, we found the exact value of error-detecting locating domination number of Mycielskian of some classes of graphs.