Hexagonal Difference Prime Labeling of Some Path Graphs

Abstract

Hexagonal difference prime labeling of vertices of a graph is the labeling of the vertices of the graph with hexagonal numbers and the edges with absolute value of the difference of the labels of the incident vertices. The greatest common incidence number (gcin) of a vertex of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is 1, then the graph admits hexagonal difference prime labeling.  Here we identify some path related graphs for hexagonal difference prime labeling.