2020/09/17 by Jason DeVito, DeVito, Jason, Amanda Niedzialomski +3
Computer Science · Engineering · #Graph Labeling and Dimension Problems #Advanced Graph Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2009.08532
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.