The study of odd graceful and odd strongly harmonious for bipartite graph

TL;DR

This paper explores the relationships between odd graceful and odd strongly harmonious graphs within bipartite graphs, establishing key implications and characterizations.

Contribution

It proves that odd strongly harmonious graphs are odd graceful and bipartite odd graceful graphs are odd strongly harmonious, clarifying their interrelations.

Findings

Odd strongly harmonious graphs are a subset of odd graceful graphs.

Bipartite odd graceful graphs are also odd strongly harmonious.

The paper establishes the implications between these graph classes.

Abstract

In this paper, we investigate odd graceful graph, odd strongly harmonious graph, bipartite graph and their relationship. We proved following results: (1) if G is odd strongly harmonious graph, then G is odd graceful graph ;(2) if G is bipartite odd graceful graph, then G is odd strongly harmonious graph.