Solving L(2,1)-Labeling Problem of Graphs using Genetic Algorithms 


Vol. 15,  No. 2, pp. 131-136, Apr.  2008
10.3745/KIPSTB.2008.15.2.131


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  Abstract

L(2,1)-labeling of a graph G is a function f: V(G) → {0, 1, 2, ...} such that f(u) ? f(v) ≥ 2 when d(u, v) = 1 and f(u) ? f(v) ≥ 1 when d(u, v) = 2. L(2,1)-labeling number of G, denoted by λ(G), is the smallest number m such that G has an L(2,1)-labeling with no label greater than m. Since this problem has been proved to be NP-complete, in this article, we develop genetic algorithms for L(2,1)-labeling problem and show that the suggested genetic algorithm peforms very efficiently by applying the algorithms to the class of graphs with known optimum values.

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[IEEE Style]

K. H. Han and C. S. Kim, "Solving L(2,1)-Labeling Problem of Graphs using Genetic Algorithms," The KIPS Transactions:PartB , vol. 15, no. 2, pp. 131-136, 2008. DOI: 10.3745/KIPSTB.2008.15.2.131.

[ACM Style]

Keun Hee Han and Chan Soo Kim. 2008. Solving L(2,1)-Labeling Problem of Graphs using Genetic Algorithms. The KIPS Transactions:PartB , 15, 2, (2008), 131-136. DOI: 10.3745/KIPSTB.2008.15.2.131.

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