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math.CO2026
Exact Dominion of the Prism Graph: Enumeration by Congruence Class via Cyclic Words
Julian Allagan
Let G_n = C_n square P_2 denote the prism (circular ladder) graph on 2n vertices. By encoding column configurations as cyclic words, domination is reduced to local Boolean constrai…
math.CO2026
Four Dominion Growth Regimes in Trees: Forcing, Fibonacci Enumeration, Periodicity, and Stability
Julian Allagan, Erin Gray, Jennifer Sawyer +1
We study the dominion zeta(G), defined as the number of minimum dominating sets of a graph G, and analyze how local forcing and boundary effects control the flexibility of optimal…