On Edge Prime Index of a Graph

Abstract

Relatively Prime Edge labeling extends the notion of prime labeling by considering edges. Prime labeling requires adjacent vertices to possess relatively prime labels, while relatively prime edge labeling requires adjacent edges to have relatively prime labels. The transformation of a coprime edge-labeled graph into a relatively prime edge-labeled graph introduces the concept of Edge Prime Index (or Relatively Prime Index). This study focuses on cases where a coprime edge-labeled graph can be converted into a relatively prime edge-labeled graph by removing certain edges from graph G, thereby establishing the concept of Edge Prime Index. Finally, the Edge Prime Index of some graphs are found.