Radio Number of Hamming Graphs of Diameter 3

Authors

Jason DeVito, University of Tennessee MartinFollow
Amanda Niedzialomski, University of Tennessee, MartinFollow
Jennifer Warren, University of Tennessee MartinFollow

Publication Date

July 2022

Abstract

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

DeVito, Jason; Niedzialomski, Amanda; and Warren, Jennifer (2022) "Radio Number of Hamming Graphs of Diameter 3," Theory and Applications of Graphs: Vol. 9: Iss. 2, Article 10.
DOI: 10.20429/tag.2022.090210
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss2/10