Total Neighborhood Prime Labeling of Join Graphs
N P Shrimali, Aswin Rathod · 2020
A total neighborhood prime graph admits a total neighborhood prime labeling. This chapter investigates total neighborhood prime labeling for some join graphs. It considers the simple, finite, connected and undirected graph with a specific vertex set and a specific edge set. The union of some graphs are neighborhood-prime graphs, and the product of some graphs are neighborhood-prime. In a neighborhood-prime labeling, edges are not considered. A specific path attached at each vertex of a cycle forms an armed crown. For any vertex, a function contains at least two consecutive numbers or consecutive odd numbers such that the greatest common divisor is equal to one.