Year: 2026
Type: article
Abstract: Let k ∈ Z+and let G = (V,E) be a connected graph of order n. An arithmetic k-radio labelingis a bijection η : V →{1, 1 + k, 1 + 2k,..., 1 + (n− 1)k} such that for any two distinct vertices u,v ∈ V , the condition |η(u)− η(v)| > diam(G)− dist(u,v) is satisfied. The least such k is defined as the arithmetic radio number of G, denoted by Ra(G). In this paper, we establish exact values of Ra(G) for several families of graphs, including paths, cycles, squares of paths, and the join of graphs. Our results contribute to the broader context of distance-constrained labeling by combining structural graph properties with arithmetic progressions in labeling.
DOI: 10.5269/bspm.80132
Institutions: Nitte University, REVA University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7222898521