A Metaheuristic Approach to the Graceful Labeling Problem

Authors:
Houra Mahmoudzadeh;Kourosh Eshghi
Affiliations:
Sharif University of Technology, Iran;Sharif University of Technology, Iran
Venue:
International Journal of Applied Metaheuristic Computing
Year:
2010

Citing 4
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Abstract

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 Ant Colony Optimization metaheuristic is proposed for finding its solutions. In this regard, the proposed algorithm is applied to different classes of graphs and the results are compared with the few existing methods inside of different literature.