Metric dimension of Andrásfai graphs

Abstract

A set W ⊆ V (G) is called a resolving set, if for each pair of distinct verticesis the distance between vertices x and y. The cardinality of a minimum resolving set for G is called the metric dimension of G and is denoted by dim M (G). This parameter has many applications in different areas. The problem of finding metric dimension is NPcomplete for general graphs but it is determined for trees and some other important families of graphs. In this paper, we determine the exact value of the metric dimension of Andrásf ai graphs, their complements and And(k) P n . Also, we provide upper and lower bounds for dim M (And(k) C n ).

Generalized Andrásfai Graphs

“…Also let x = 9 and y = 6. Then x − y = 3 ≡ −1 (mod 4), but [6] ∼ [9], as S = {[1], [5], [9], [13]}. This observation motivates us to get a better understanding of the adjacency condition in light of Lemma 2.1.…”

“…As circulant graphs are an important class of interconnection networks in parallel and distributed computing, two important questions pertaining to generalized Andrásfai graphs for further research are to determining its metric dimension and spectrum. It is worth mentioning that recently in [6], authors computed the metric dimension of Andrásfai graphs.…”