## Abstract

A fixed interconnection parallel architecture is characterized by a graph, with vertices corresponding to processing nodes and edges representing communication links. An ordered set R of nodes in a graph G is said to be a resolving set of G if every node in G is uniquely determined by its vector of distances to the nodes in R. Each node in R can be thought of as the site for a sonar or loran station, and each node location must be uniquely determined by its distances to the sites in R. A fault-tolerant resolving set R for which the failure of any single station at node location v in R leaves us with a set that still is a resolving set. The metric dimension (resp. fault-tolerant metric dimension) is the minimum cardinality of a resolving set (resp. fault-tolerant resolving set). In this article, we study the metric and fault-tolerant dimension of certain families of interconnection networks. In particular, we focus on the fault-tolerant metric dimension of the butterfly, the Benes and a family of honeycomb derived networks called the silicate networks. Our main results assert that three aforementioned families of interconnection have an unbounded fault-tolerant resolvability structures. We achieve that by determining certain maximal and minimal results on their fault-tolerant metric dimension.

Original language | English |
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Article number | 9162022 |

Pages (from-to) | 145435-145445 |

Number of pages | 11 |

Journal | IEEE Access |

Volume | 8 |

DOIs | |

Publication status | Published - 2020 |

## Keywords

- Graph theory
- NP-complete problems
- fault-tolerant metric dimension
- interconnection networks
- metric dimension

## ASJC Scopus subject areas

- General Computer Science
- General Materials Science
- General Engineering