Channel Assignment Algorithms for Graphs in the Plane with Graceful Constraints

An assignment of integer numbers to the vertices of a given graph under certain conditions is referred to as a graph labeling. The assignment of labels from the set {0,1,2,...,2 1} q to the vertices of G (with ( ) G n V vertices and ( ) q E G edges) such that, when each edge has assigned a label defined by the absolute difference of its end-points, the resulting edge labels are 1,3 ,2 1 q is referred to as an odd graceful labeling of the graph. In 2000, Kathiresan [13] used the notation ; n m P to denote the graph (spider graph) obtained by identifying the end points of m paths each one has length n , we use the notation m n C ; to denote the graph (closed spider) obtained by identifying the other end points of the graph ; n m P . In this article, we present three algorithms to show how to odd gracefully label the vertices and the edges of the following graphs; 2 1; , 1 5, 2 r m P r m , the closed spider m n C ; , and the graphs obtained by joining one or two paths m P to each vertex of the path n P .