DisCoMath Seminar: Efficient Domination in Regular Graphs
Efficient Domination in Regular Graphs
Dr. Brendan Rooney
Assistant Professor
School of Mathematical Sciences, RIT
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Abstract:
A function f : V (G)→{0,…,j} is an efficient (j, k)-dominating function on G if ∑u∈N[v] f (u) = k for all v ∈ V (G) (here N [v] = N (v) ∪ {v} is the closed neighbourhood of v). Efficient (j, k)-domination was introduced by Rubalcaba and Slater (2007) as a generalization of perfect domination, and efficient k-domination. We look at efficient domination on regular graphs, applying some standard tools from linear algebra and algebraic graph theory. Using these ideas we give a partial characterization of the values k for which the Hamming graphs H(q,d) are efficiently (1, k)-dominatable. This extends the theorem of Tietavainen-van Lint-Leont’ev-Zinov’ev characterizing codes that meet the sphere packing bound.
Speaker Bio:
Dr. Rooney is an Assistant Professor in the School of Mathematical Sciences at RIT. He completed his Ph.D. in Combinatorics and Optimization at the University of Waterloo, Ontario, Canada. Prior to joining RIT, he was a Visiting Assistant Professor in the Department of Mathematical Sciences at Korea Advanced Institute of Science and Technology (KAIST) for three years. Dr. Rooney’s research interests include Graph Theory, Combinatorics and Combinatorial Optimization.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
Keep up with DisCoMath Seminars on the DisCoMathS webpage.
Event Snapshot
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This is an RIT Only Event
Interpreter Requested?
No