Distinct Prime Distance Labeling of Certain Graphs

Abstract

Graph labeling is an area of extensive research with several different labelings having been introduced motivated by many application problems. A labeling, called prime distance labeling, assigns integer labels to the vertices of a graph such that the absolute difference of the labels of any two adjacent vertices is a prime number. Here, we introduce the notion of distinct prime distance labeling. A prime distance labeling of a graph G is distinct if the absolute differences of the integer labels of adjacent vertices are distinct prime numbers. In this paper, we derive certain general results concerning distinct prime distance labeling and examine such a labeling for certain classes of graphs.