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Channel Assignment Algorithms for Graphs in the Plane with Graceful Constraints
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 18 - Number 8 |
| Year of Publication: 2011 |
| Authors: M. Ibrahim Moussa |
10.5120/2301-2615
|
M. Ibrahim Moussa . Channel Assignment Algorithms for Graphs in the Plane with Graceful Constraints. International Journal of Computer Applications. 18, 8 ( March 2011), 35-42. DOI=10.5120/2301-2615
Abstract
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,...,2q-1} to the vertices of G (with n=|V(G)| 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...,2q-1} is referred to as an odd graceful labeling of the graph. In 2000, Kathiresan [13] used the notation Pn;m to denote the graph (spider graph) obtained by identifying the end points of m paths each one has length n , we use the notation Cn;m to denote the graph (closed spider) obtained by identifying the other end points of the graph Pn;m. In this article, we present three algorithms to show how to odd gracefully label the vertices and the edges of the following graphs;P2r+1;m, 1≤ r ≤ 5, m ≥ 2, the closed spider Cn;m, and the graphs obtained by joining one or two paths Pm to each vertex of the path Pn.
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