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Ars Combinatoria

  • Research article

Edge Domination and Secure Edge Domination in Mycielski Graph of Trees

Nayana P G1, Chithra M R2
1Department of Mathematics, Amrita Vishwa Vidyapeetham, Kochi, India
2Department of Mathematics, University of Kerala, Thiruvananthapuram, 695581, Kerala, India
  • Received: 04/12/2019
  • Accepted: 10/12/2020
  • Published: 30/09/2024

Abstract

The secure edge dominating set of a graph \( G \) is an edge dominating set \( F \) with the property that for each edge \( e \in E-F \), there exists \( f \in F \) adjacent to \( e \) such that \( (F-\{f\})\cup \{e\} \) is an edge dominating set. In this paper, we obtained upper bounds for edge domination and secure edge domination number for Mycielski of a tree.

Keywords: Edge domination, Secure edge domination, Mycielski graph, Trees, Graph theory, Domination in graphs
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Citation
Nayana P G, Chithra M R. Edge Domination and Secure Edge Domination in Mycielski Graph of Trees[J], Ars Combinatoria, Volume 160. 205-209. DOI: https://doi.org/10.61091/ars-160-16.