Opuscula Math. 29, no. 4 (2009), 393-397
http://dx.doi.org/10.7494/OpMath.2009.29.4.393

Opuscula Mathematica

α2-labeling of graphs

Dalibor Fronček

Abstract. We show that if a graph $$G$$ on $$n$$ edges allows certain special type of rosy labeling (a.k.a. $$\rho$$-labeling), called $$\alpha_2$$-labeling, then for any positive integer $$k$$ the complete graph $$K_{2nk+1}$$ can be decomposed into copies of $$G$$. This notion generalizes the $$\alpha$$-labeling introduced in 1967 by A. Rosa.

Keywords: graph decomposition, graph labeling.

Mathematics Subject Classification: 05C78.

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• Dalibor Fronček
• University of Minnesota Duluth, Department of Mathematics and Statistics, 1117 University Dr., Duluth, MN 55812, U.S.A.
• Revised: 2009-07-05.
• Accepted: 2009-07-06.