Algorithm-based radio labeling for optimal channel assignment in outerplanar graphs

IntroductionRadio labeling of graphs extends the channel assignment problem by assigning non-negative integers to vertices of a connected graph G such that |h(℘)−h(𝓆)|≥diam(ℊ)+1−d(℘, 𝓆). The objective is to minimize the span, leading to the radio number rn(G).MethodsWe consider a class of outerplanar graphs with vertex set {u1, v1, x1, …, xn, y1, …, yn} and a structured edge set combining path and matching edges. Analytical bounds and a constructive labeling algorithm are developed.ResultsLower and upper bounds for rn(G) are derived, and the proposed algorithm yields feasible radio labelings with near-optimal span.DiscussionThe results highlight that the structure of outerplanar graphs enables efficient labeling strategies and provide a basis for extending radio labeling techniques to broader graph classes.