Further results on the radio number for some construction of the path, complete, and complete bipartite graphs

Abstract

Let G be a connected graph with diam(G). Then d(u,v) indicates the distance of u and v in G. For any pair of distinct vertices u,v of G, mapping from c:V(G)→N such that dG(u,v)+|c(u)−c(v)|≥diam(G)+1. The maximum label assigned to any vertex of G under a radio labeling c is known as the span of c. The radio number rn(G) of G is defined as the minimum span among all possible radio labelings of G. This paper aims to determine the radio number rn(c) for specific constructed families of graphs with diameter 3, such as P22(N(m,n)), K3,m(Knc), K3,m(nP3), K3,3(2K1,n), and K5(F3n).

Keywords

• Radio labeling
• Radio number
• Path
• Complete
• Complete bipartite
• Diameter three labeling