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