Metric Dimension of Flower Graphs

Abstract

The metric dimension of a connected graph G is the smallest number of nodes (resolving set) required to identify all other nodes based on shortest path distances uniquely. The notion of resolving set is significant in robotic navigation and to construct various plan of action for the mastermind game.A resolving set of G is a set \(S\subset V (G)\) if some vertices of S resolve every pair of nodes u and v of G. A metric basis represents the lowest number of nodes in a resolving set. In this research article we characterize the metric dimension and distance matrix of sunflower graphs and flower snarks.