4 papers
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…
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…
Statistical and Machine Learning Analysis of Traffic Accidents on US 158 in Currituck County: A Comparison with HSM Predictions
Jennifer Sawyer, Julian Allagan
This study extends previous hotspot and Chi-Square analysis by Sawyer \cite{sawyer2025hotspot} by integrating advanced statistical analysis, machine learning, and spatial modeling…
Multi-Method Analysis of Mathematics Placement Assessments: Classical, Machine Learning, and Clustering Approaches
Julian D. Allagan, Dasia A. Singleton, Shanae N. Perry +2
This study evaluates a 40-item mathematics placement examination administered to 198 students using a multi-method framework combining Classical Test Theory, machine learning, and…