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math.CO2025
Maximal bipartite graphs with a unique minimum dominating set
Garrison Koch, Darren Narayan
In 2003, Fischermann et al. considered the maximum size of \textit{uniquely-dominatable} graphs, graphs whose dominating number is realized only by a unique dominating set. They co…
math.CO2023
On the $nk-attack Roman Dominating Number of a Graph
Garrison Koch, Nathan Shank
Given a graph , the dominating number of a graph is the minimum size of a vertex set, , so that every vertex in the graph is either in or is adjacent…