Harmonious Labelings Via Cosets and Subcosets
Jared Painter, Holleigh Landers, Walker Mattox · Theory and Applications of Graphs · 2022
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.