A Comparative Study of Graceful Labeling and Harmonious Labeling for Business Model which can be obtained by Quaternary Tree - Priyanka Bhalerao, Seema Bagora (International Journal of Control and Automation, 2020)
In the mathematical discipline of graph theory, graph labeling is the assignment of labels, traditionally represented by integers, to edges or vertices of a graph. There are many graph labeling techniques like prime labeling, edge graceful labeling, graceful labeling, cordial labeling and harmonious labeling. All these labeling have their own specialty to label graphs. With their own properties, they make themselves unique. All these types have lots of applications in social marketing and many other fields.  In this paper we compare two types of labeling methodologies namely graceful labeling and harmonious labeling and apply it to our business model, which can be constructed by k-ary trees.