Conclusion
In our research, we were able to classify some types of graphs, many of which are shown here, as harmonious or locally harmonious. Hopefully this research will result in us having a better understanding of both infinite graphs and of harmonious labelings. Also the new graph Dn we defined and the type of labeling we defined, locally harmonious labeling, could also lead to new findings and a better understanding of various topics in graph theory.
Future Studies
Some of the things that could be studied in the future include showing that all infinite trees are locally harmonious, which we suspect to be the case, and considering finite and infinite graphs with cycles in them for locally harmonious labeling. Also, more research on whether known familes of infinite graphs are harmonious will hopefully be pursued.