Discrete Mathematics and Combinatorics Commons^™

Radio Number Of Hamming Graphs Of Diameter 3, Jason Devito, Amanda Niedzialomski, Jennifer Warren

Theory and Applications of Graphs

For G a simple, connected graph, a vertex labeling f:V(G) → Z+ is called a radio labeling of G if it satisfies |f(u)-f(v)|≥ diam(G)+1-d(u,v) for all distinct vertices u,v ∈ V(G). The radio number of G is the minimal span over all radio labelings of G. If a bijective radio labeling onto {1,2,…|V(G)|} exists, G is called a radio graceful graph. We determine the radio number of all diameter 3 Hamming graphs and show that an infinite subset of them is radio graceful.