Applications of mathematical programming in graceful labeling of graphs
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 mathematic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2004-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X04310065 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |