On The Secure Domination of Mycielskian Graphs
Kiran R. Bhutani, Anthony Christiana, Peter Ulrickson
TL;DR
This paper investigates the secure domination number in Mycielskian graphs, providing bounds, exact values for key graph families, and constructions for specific domination parameters.
Contribution
It introduces new bounds and exact calculations for secure domination numbers in Mycielskian graphs, expanding understanding of domination parameters in this graph class.
Findings
Derived bounds for secure domination numbers
Computed secure domination numbers for key graph families
Constructed graphs with specific domination parameter values
Abstract
We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for Mycielskians of important families of graphs, and construct families of graphs realizing particular values of (secure) domination parameters.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory