Metric dimension and edge metric dimension of windmill graphs

Pradeep Singh; Sahil Sharma; Sunny Kumar Sharma; Vijay Kumar Bhat; Pradeep Singh; Sahil Sharma; Sunny Kumar Sharma; Vijay Kumar Bhat

doi:10.3934/math.2021531

AIMS Mathematics

2021, Volume 6, Issue 9: 9138-9153. doi: 10.3934/math.2021531

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Research article Special Issues

Metric dimension and edge metric dimension of windmill graphs

School of Mathematics, Shri Mata Vaishno Devi University, J & K 182320 , India

Received: 13 April 2021 Accepted: 15 June 2021 Published: 18 June 2021
MSC : 05C12, 05C40, 05C76, 05C85

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.
- resolving set,
- metric dimension,
- edge metric dimension,
- edge metric basis,
- French windmill graph,
- Dutch windmill graph
Citation: Pradeep Singh, Sahil Sharma, Sunny Kumar Sharma, Vijay Kumar Bhat. Metric dimension and edge metric dimension of windmill graphs[J]. AIMS Mathematics, 2021, 6(9): 9138-9153. doi: 10.3934/math.2021531

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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.

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