$On regular handicap graphs of order $n \equiv 0$ mod 8$

On regular handicap graphs of order $n \equiv 0$ mod 8

A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection <span class=&quo...

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Main Authors:	Dalibor Froncek, Aaron Shepanik
Format:	Article
Language:	English
Published:	Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2018-10-01
Series:	Electronic Journal of Graph Theory and Applications
Subjects:	graph labeling, handicap labeling, regular graphs, tournament scheduling
Online Access:	https://www.ejgta.org/index.php/ejgta/article/view/506

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spelling	doaj-4a9910672de947d38d37f7f9d7c4b4f62021-03-11T01:13:05ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872018-10-016220821810.5614/ejgta.2018.6.2.1117On regular handicap graphs of order $n \equiv 0$ mod 8Dalibor Froncek0Aaron Shepanik1Department of Mathematics and Statistics, University of Minnesota Duluth Duluth, USADepartment of Mathematics and Statistics, University of Minnesota Duluth Duluth, USA<p>A handicap distance antimagic labeling of a graph <span class="math"><em>G</em> = (<em>V</em>, <em>E</em>)</span> with <span class="math"><em>n</em></span> vertices is a bijection <span class="math"><em>f̂</em> : <em>V</em> → {1, 2, …, <em>n</em>}</span> with the property that <span class="math"><em>f̂</em>(<em>x</em><sub><em>i</em></sub>) = <em>i</em></span>, the <span><em>weight</em></span> <span class="math"><em>w</em>(<em>x</em><sub><em>i</em></sub>)</span> is the sum of labels of all neighbors of <span class="math"><em>x</em><sub><em>i</em></sub></span>, and the sequence of the weights <span class="math"><em>w</em>(<em>x</em><sub>1</sub>), <em>w</em>(<em>x</em><sub>2</sub>), …, <em>w</em>(<em>x</em><sub><em>n</em></sub>)</span> forms an increasing arithmetic progression. A graph <span class="math"><em>G</em></span> is a <span><em>handicap distance antimagic graph</em></span> if it allows a handicap distance antimagic labeling. We construct <span class="math"><em>r</em></span>-regular handicap distance antimagic graphs of order <span class="math">$n \equiv 0 \pmod{8}$</span> for all feasible values of <span class="math"><em>r</em></span>.</p>https://www.ejgta.org/index.php/ejgta/article/view/506graph labeling, handicap labeling, regular graphs, tournament scheduling
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dalibor Froncek Aaron Shepanik
spellingShingle	Dalibor Froncek Aaron Shepanik On regular handicap graphs of order $n \equiv 0$ mod 8 Electronic Journal of Graph Theory and Applications graph labeling, handicap labeling, regular graphs, tournament scheduling
author_facet	Dalibor Froncek Aaron Shepanik
author_sort	Dalibor Froncek
title	On regular handicap graphs of order $n \equiv 0$ mod 8
title_short	On regular handicap graphs of order $n \equiv 0$ mod 8
title_full	On regular handicap graphs of order $n \equiv 0$ mod 8
title_fullStr	On regular handicap graphs of order $n \equiv 0$ mod 8
title_full_unstemmed	On regular handicap graphs of order $n \equiv 0$ mod 8
title_sort	on regular handicap graphs of order $n \equiv 0$ mod 8
publisher	Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
series	Electronic Journal of Graph Theory and Applications
issn	2338-2287
publishDate	2018-10-01
description	<p>A handicap distance antimagic labeling of a graph <span class="math"><em>G</em> = (<em>V</em>, <em>E</em>)</span> with <span class="math"><em>n</em></span> vertices is a bijection <span class="math"><em>f̂</em> : <em>V</em> → {1, 2, …, <em>n</em>}</span> with the property that <span class="math"><em>f̂</em>(<em>x</em><sub><em>i</em></sub>) = <em>i</em></span>, the <span><em>weight</em></span> <span class="math"><em>w</em>(<em>x</em><sub><em>i</em></sub>)</span> is the sum of labels of all neighbors of <span class="math"><em>x</em><sub><em>i</em></sub></span>, and the sequence of the weights <span class="math"><em>w</em>(<em>x</em><sub>1</sub>), <em>w</em>(<em>x</em><sub>2</sub>), …, <em>w</em>(<em>x</em><sub><em>n</em></sub>)</span> forms an increasing arithmetic progression. A graph <span class="math"><em>G</em></span> is a <span><em>handicap distance antimagic graph</em></span> if it allows a handicap distance antimagic labeling. We construct <span class="math"><em>r</em></span>-regular handicap distance antimagic graphs of order <span class="math">$n \equiv 0 \pmod{8}$</span> for all feasible values of <span class="math"><em>r</em></span>.</p>
topic	graph labeling, handicap labeling, regular graphs, tournament scheduling
url	https://www.ejgta.org/index.php/ejgta/article/view/506
work_keys_str_mv	AT daliborfroncek onregularhandicapgraphsofordernequiv0mod8 AT aaronshepanik onregularhandicapgraphsofordernequiv0mod8
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On regular handicap graphs of order $n \equiv 0$ mod 8

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