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 language | English |
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Article number | 78 |
Journal | Mathematics |
Volume | 7 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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