Some Results on Relatively Prime Edge Labeled Graph - Janani, R.; Ramachandran, T. (Communications in Mathematics and Applications, 2023)
Prime labeling and relatively prime edge labeling have the same idea for labeling the general graph \(G\). Prime labeling labels the vertices of the general graph in such a way that adjacent vertices receive relatively prime labels. Similarly, relatively prime edge labeling, labels the edges in a way that the adjacent edges have relatively prime labels. Also, there are graphs that do not have relatively prime edge labeling. Hence the concept of relatively prime index is introduced, which finds the minimum number of edges to be removed from \(G\) to make it a relatively prime edge labeled graph. The main purpose of the current study is to discuss some results on the topic of relatively prime edge labeled graphs and relatively prime index.