THE HARMONIOUS, ODD HARMONIOUS, AND EVEN HARMONIOUS LABELING

Abstract

Suppose is a simple and connected graph with edges. A harmonious labeling on a graph is an injective function (formula presented)so that there exists a bijective function (formula presented) where (formula presented), for each (formula presenetd) An odd harmonious labeling on a graph is an injective function from V(G) to non-negative integer set less than so that there is a function (formula presented) where (formula presented) for every (formula presented) An even harmonious labeling on a graph is an injective function (formula presented) so that there is a bijective function (formula presented) where (formula presented) for each (formula presented). 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)