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.
Mari et al. (Wed,) studied this question.