Opuscula Math. 30, no. 1 (2010), 61-67
http://dx.doi.org/10.7494/OpMath.2010.30.1.61

Opuscula Mathematica

# 2-splittable and cordial graphs

Sylwia Cichacz

Abstract. E. Miller and G. E. Stevens proved in [E. Miller, G. E. Stevens, Some graphs for which even size is sufficient for splittability, Congressus Numerantium 173 (2005), 137–147] the existence of certain families of $$2$$-splittable caterpillars. In this paper we characterize other families of $$2$$-splittable caterpillars. Moreover, we show that for some of them there exists a friendly labeling inducing two isomorphic subgraphs.

Keywords: cordial graphs, $$2$$-splittable graphs.

Mathematics Subject Classification: 05C78.

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• Sylwia Cichacz
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
• University of Minnesota Duluth, Duluth, MN 55812-3000 U.S.A.
• Revised: 2009-09-07.
• Accepted: 2009-09-11.