Alpha labelings of full hexagonal caterpillars

Abstract

Barrientos and Minion (2015) introduced the notion of generalized snake polyomino graphs and proved that when the cells are either squares or hexagons, then they admit an alpha labeling. Froncek et al. (2014) generalized the notion by introducing straight simple polyominal caterpillars with square cells and proved that they also admit an alpha labeling. We introduce a similar family of graphs called full hexagonal caterpillars and prove that they also admit an alpha labeling. This implies that every full hexagonal caterpillar with n edges decomposes the complete graph K2kn+1 for any positive integer k.

Keywords

• Alpha labeling
• Graceful labeling
• Graph decomposition