The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994. However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.

Graph labeling traces its origin to the famous conjecture that all trees are graceful presented by A.Rosa in 1966. In recent years, many research papers on graceful graph have been published. In this survey we have collected studies on the gracefulness of the directed circuit ~ Cm and the union graph of mutually non-intersecting ~ Cm, the digraph n · ~ Cm, the digraph n − ~ Cm, the union of the...

In graph theory, a graceful labeling of a graph G = (V, E) with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints. In this paper, the well-known graceful labeling problem of graphs is represented as an optimization problem, and an algorithm based on An...

A tree with n vertices is called graceful if there exists a labeling of its vertices with the numbers from 1 to n such that the set of absolute values of the differences of the numbers assigned to the ends of each edge is the set {1, 2, .., n− 1}. The problem of whether or not all trees are graceful is still open. In this paper, we give an extensive survey of most of the results related to this...