Gracefully Harmonious Graphs

Abstract

Labelling problems are very useful in modelling, solving problems in other areas and enhance the study of algebraic structures. Nowadays, a more practical, accurate and efficient way of labeling a graph is using some mathematical methods like integer programming or constraint programming. This will improve the scope and quality of research. Here, considering the applications of Graceful and Harmonious labelings, we introduce a few new types of labeling, namely, gracefully harmonious labeling, gracefully felicitous labeling, gracefully elegant labeling, gracefully strongly c-elegant labeling and gracefully semi-harmonious labeling. In this paper, we prove that some complete multi-partite graphs is gracefully harmonious, gracefully felicitous and gracefully semi-harmonious. Keywords: Labeling; multi-partite graph; gracefully harmonious; gracefully felicitous; gracefully semi-harmonious. 2010 Mathematics Subject Classification: 05C78