A Metaheuristic Approach to the Graceful Labeling Problem

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Author(s): Houra Mahmoudzadeh (Sharif University of Technology, Iran)and Kourosh Eshghi (Sharif University of Technology, Iran)
Copyright: 2012
Pages: 16
Source title: Modeling, Analysis, and Applications in Metaheuristic Computing: Advancements and Trends
Source Author(s)/Editor(s): Peng-Yeng Yin (Ming Chuan University, Taiwan)
DOI: 10.4018/978-1-4666-0270-0.ch013

Keywords: Algorithms / Artificial Intelligence / Computer Science & IT / Information Science Reference

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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.

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