Prime Graceful Chromatic Number of Diverse Graphs

Abstract

In this paper, prime graceful coloring is introduced which aims to incorporate principles of prime and graceful coloring. The prime graceful coloring of star, path, cycle, friendship, pan and bistar graphs are proposed. This new approach is related to the prime graceful chromatic number which represent the fewest colors needed to color any graph adhering to the principles of prime graceful coloring. Also, the efficiency of new coloring are analyzed with the examples.