THE HARMONIOUS, ODD HARMONIOUS, AND EVEN HARMONIOUS LABELING

Suppose  is a simple and connected graph with  edges. A harmonious labeling on a graph  is  an injective function  so that there exists a bijective function  where  for each  An odd harmonious labeling on a graph  is an injective function  from  to non-negative integer set less than  so that there is a function  where  for every  An even harmonious labeling on a graph  is an injective function  so that there is a bijective function   where  for each . In this paper, we discuss how to build new labeling (harmonious, odd harmonious, even harmonious) based on the existing labeling (harmonious, odd harmonious, even harmonious)