Harmonious Labelings Via Cosets and Subcosets

Authors

Jared L. Painter, University of North AlabamaFollow
Holleigh C. Landers, University of North AlabamaFollow
Walker M. Mattox, University of North AlabamaFollow

Publication Date

July 2022

Abstract

In [Abueida, A. and Roblee, K., More harmonious labelings of families of disjoint unions of an odd cycle and certain trees, J. Combin. Math. Combin. Comput., 115 (2020), 61-68] it is shown that the disjoint union of an odd cycle and certain paths is harmonious, and that certain starlike trees are harmonious using properties of cosets for a particular subgroup of the integers modulo m, where m is the number of edges of the graph. We expand upon these results by first exploring the numerical properties when adding values from cosets and subcosets in the integers modulo m. We will then show that these properties may be used to harmoniously label graphs involving a more complex starlike tree, which we will call the snowflake graph.

Creative Commons License

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

Recommended Citation

Painter, Jared L.; Landers, Holleigh C.; and Mattox, Walker M. (2022) "Harmonious Labelings Via Cosets and Subcosets," Theory and Applications of Graphs: Vol. 9: Iss. 2, Article 4.
DOI: 10.20429/tag.2022.090204
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss2/4