On some new edge odd graceful graphs

Abstract

Given a simple connected undirected graph G and let k be the maximum number of its vertices and its edges. Let f be a bijective labeling from the set of its edges to the set of odd integers from 1 up to 2q − 1, where q is the number of edges of G. The labeling f is called an edge odd graceful labeling on G if the weights of any two different vertices are different, where the weight of a vertex v is defined as the sum mod(2k) of all labels of edges that are incident to v. A graph is called an edge odd graceful graph if it admits an edge odd graceful labeling. In this paper, we show that there are some new classes of graphs that are edge odd graceful.