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

# α2-labeling of graphs

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.