Metric dimension and edge metric dimension of windmill graphs

Abstract

Graph invariants provide an amazing tool to analyze the abstract structures of graphs. Metric dimension and edge metric dimension as graph invariants have numerous applications, among them are robot navigation, pharmaceutical chemistry, etc. In this article, we compute the metric and edge metric dimension of two classes of windmill graphs such as French windmill graph and Dutch windmill graph, and also certain generalizations of these graphs.

Keywords

• resolving set
• metric dimension
• edge metric dimension
• edge metric basis
• french windmill graph
• dutch windmill graph