Alpha labelings of full hexagonal caterpillars

Dalibor Froncek

doi:10.1016/j.akcej.2016.03.003

Alpha labelings of full hexagonal caterpillars

Dalibor Froncek

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 K_2kn+1 for any positive integer k.

Original language	English (US)
Pages (from-to)	85-89
Number of pages	5
Journal	AKCE International Journal of Graphs and Combinatorics
Volume	13
Issue number	1
DOIs	https://doi.org/10.1016/j.akcej.2016.03.003
State	Published - Apr 1 2016

Bibliographical note

Publisher Copyright:
© 2016 Kalasalingam University.

Keywords

Alpha labeling
Graceful labeling
Graph decomposition

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10.1016/j.akcej.2016.03.003

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AB - 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.

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KW - Graceful labeling

KW - Graph decomposition

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ER -

Alpha labelings of full hexagonal caterpillars

Abstract

Bibliographical note

Keywords

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