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Fault-Tolerant Resolvability and Extremal Structures of Graphs

Authors
  • Raza, Hassan
  • Hayat, Sakander
  • Imran, Muhammad
  • Pan, Xiang-Feng
Publication Date
Jan 14, 2019
Source
MDPI
Keywords
Language
English
License
Green
External links

Abstract

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.

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