Journal of Applied Mathematics
Volume 2004 (2004), Issue 1, Pages 1-8
doi:10.1155/S1110757X04310065
Applications of mathematical programming in graceful labeling of graphs
Department of Industrial Engineering, Sharif University of Technology, Tehran 11365-9414, Iran
Received 19 October 2003; Revised 31 December 2003
Copyright © 2004 Kourosh Eshghi and Parham Azimi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Graceful labeling is one of the best known labeling methods of
graphs. Despite the large number of papers published on the
subject of graph labeling, there are few particular techniques to
be used by researchers to gracefully label graphs. In this paper,
first a new approach based on the mathematical programming
technique is presented to model the graceful labeling problem.
Then a “branching method” is developed to solve the problem for
special classes of graphs. Computational results show the
efficiency of the proposed algorithm for different classes of
graphs. One of the interesting results of our model is in the
class of trees. The largest tree known to be graceful has at most
27 vertices but our model can easily solve the graceful labeling
for trees with 40 vertices.