On radio graceful Hamming graphs of any diameter
-
Amanda Niedzialomski
Abstract
We show that Hamming graphs of diameter D are radio graceful provided that each component of the Hamming graph is a complete graph with at least D vertices. This generalizes the results known previously for diameters D = 2 and D = 3 and for general D with the assumption that the components of the Hamming graph have the same or pairwise relatively prime numbers of vertices.
Originally published in Diskretnaya Matematika (2024) 36, №3, 105–114 (in Russian).
References
[1] DeVito J., Niedzialomski A., Warren J., “Radio number of Hamming graphs of diameter 3”, Theory Appl. Graphs, 9:2 (2022), Article 10, 13 pp.10.20429/tag.2022.090210Search in Google Scholar
[2] Jacob J., Laskar R., Villalpando J., “ On the irreducible no-hole L(2, 1) coloring of bipartite graphs and Cartesian products”, J. Combin. Math. Combin. Comput., 78 (2011), 49–64.Search in Google Scholar
[3] Niedzialomski A, “ Radio graceful Hamming graphs”, Discuss. Math. Graph Theory, 36:4 (2016), 1007–1020.10.7151/dmgt.1910Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the matching arrangement of a graph and properties of its characteristic polynomial
- Realization of even permutations of even degree by products of four involutions without fixed points
- On implicit extensions in many-valued logic
- On radio graceful Hamming graphs of any diameter
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»
- Resistance distance and Kirchhoff index of two kinds of double join operations on graphs
Articles in the same Issue
- Frontmatter
- On the matching arrangement of a graph and properties of its characteristic polynomial
- Realization of even permutations of even degree by products of four involutions without fixed points
- On implicit extensions in many-valued logic
- On radio graceful Hamming graphs of any diameter
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»
- Resistance distance and Kirchhoff index of two kinds of double join operations on graphs
