Fault-tolerant resolvability and extremal structures of graphs

Hassan Raza, Sakander Hayat, Muhammad Imran, Xiang Feng Pan

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs with fault-tolerant metric dimension n, n - 1, and 2, which are the lower and upper extremal cases. Furthermore, in the first part of the paper, a method is presented to locate fault-tolerant resolving sets by using classical resolving sets in graphs. The second part of the paper applies the proposed method to three infinite families of regular graphs and locates certain fault-tolerant resolving sets. By accumulating the obtained results with some known results in the literature, we present certain lower and upper bounds on the fault-tolerant metric dimension of these families of graphs. As a byproduct, it is shown that these families of graphs preserve a constant fault-tolerant resolvability structure.

Original languageEnglish
Article number78
JournalMathematics
Volume7
Issue number1
DOIs
Publication statusPublished - Jan 14 2019

Keywords

  • Anti-prism graphs
  • Extended Petersen graphs
  • Fault-tolerant resolving set
  • Resolving set
  • Squared cycle graphs

ASJC Scopus subject areas

  • General Mathematics

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