Roman Labels Yield One-Round Power Domination

Abstract

This preprint proves that, for every finite simple graph without isolated vertices, the power domination number is at most half the Roman domination number, rounded down. More strongly, any Roman dominating function of weight w yields a sensor set of size at most floor(w/2) that observes the graph after initial domination and at most one parallel forcing round.The paper gives a constructive proof, examples showing that the coefficient is sharp, a residual-completion bound, and an adjusted inequality for graphs with isolated vertices. The main statement addresses a candidate in the AutoGraphForge audit. Manuscript source and computational inputs accompany the paper; verification software is supplied separately. Finite computational checks supplement the proof and are not a substitute for it.Author: Seth Christopher, Independent Researcher. Scientific version 1.0.0. Preprint; not independently peer reviewed. No claim of global priority or proof-assistant certification is made.The manuscript and authored supporting evidence are offered under CC BY 4.0 to the extent the author holds applicable rights. Third-party works retain their own rights.AI assistance: ChatGPT substantially assisted with target selection, mathematical development, source research, verification software, testing, and manuscript preparation. Aurelia, Selene, and Mica performed computational roles; they are not coauthors or independent reviewers. Seth Christopher is the sole author responsible for the submitted content.