Skolem Number of Cycles and Grid Graphs

A Skolem sequence can be thought of as a labelled path where two vertices with the same label are that distance apart. This concept has naturally been generalized to labellings of other graphs, but always using at most two of any integer label. Given that more than two vertices can be mutually dista...

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Autores principales:	Braxton Carrigan, John Asplund
Formato:	article
Lenguaje:	EN
Publicado:	Georgia Southern University 2021
Materias:	skolem sequence skolem labelling Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/42dcc40fa20445f9991e4235ad36417e
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spelling	oai:doaj.org-article:42dcc40fa20445f9991e4235ad36417e2021-11-16T16:59:16ZSkolem Number of Cycles and Grid Graphs2470-985910.20429/tag.2021.080204https://doaj.org/article/42dcc40fa20445f9991e4235ad36417e2021-08-01T00:00:00Zhttps://digitalcommons.georgiasouthern.edu/tag/vol8/iss2/4https://doaj.org/toc/2470-9859A Skolem sequence can be thought of as a labelled path where two vertices with the same label are that distance apart. This concept has naturally been generalized to labellings of other graphs, but always using at most two of any integer label. Given that more than two vertices can be mutually distance d apart, we define a new generalization of a Skolem sequences on graphs that we call proper Skolem labellings. This brings rise to the question; ``what is the smallest set of consecutive positive integers we can use to proper Skolem label a graph?'' This will be known as the Skolem number of the graph. In this paper we give the Skolem number for cycles and grid graphs, while also providing other related results along the way.Braxton CarriganJohn AsplundGeorgia Southern Universityarticleskolem sequenceskolem labellingMathematicsQA1-939ENTheory and Applications of Graphs, Vol 8, Iss 2 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	skolem sequence skolem labelling Mathematics QA1-939
spellingShingle	skolem sequence skolem labelling Mathematics QA1-939 Braxton Carrigan John Asplund Skolem Number of Cycles and Grid Graphs
description	A Skolem sequence can be thought of as a labelled path where two vertices with the same label are that distance apart. This concept has naturally been generalized to labellings of other graphs, but always using at most two of any integer label. Given that more than two vertices can be mutually distance d apart, we define a new generalization of a Skolem sequences on graphs that we call proper Skolem labellings. This brings rise to the question; ``what is the smallest set of consecutive positive integers we can use to proper Skolem label a graph?'' This will be known as the Skolem number of the graph. In this paper we give the Skolem number for cycles and grid graphs, while also providing other related results along the way.
format	article
author	Braxton Carrigan John Asplund
author_facet	Braxton Carrigan John Asplund
author_sort	Braxton Carrigan
title	Skolem Number of Cycles and Grid Graphs
title_short	Skolem Number of Cycles and Grid Graphs
title_full	Skolem Number of Cycles and Grid Graphs
title_fullStr	Skolem Number of Cycles and Grid Graphs
title_full_unstemmed	Skolem Number of Cycles and Grid Graphs
title_sort	skolem number of cycles and grid graphs
publisher	Georgia Southern University
publishDate	2021
url	https://doaj.org/article/42dcc40fa20445f9991e4235ad36417e
work_keys_str_mv	AT braxtoncarrigan skolemnumberofcyclesandgridgraphs AT johnasplund skolemnumberofcyclesandgridgraphs
_version_	1718426295439720448

Skolem Number of Cycles and Grid Graphs

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