<abstract xmlns="http://www.w3.org/1999/xhtml"><p>An <italic>antimagic labeling</italic> of a directed graph <italic>D</italic> with <italic>m</italic> arcs is a bijection from the set of arcs of <italic>D</italic> to {1, …, <italic>m</italic>} such that all oriented vertex sums of vertices in <italic>D</italic> are pairwise distinct, where the <italic>oriented vertex sum</italic> of a vertex <italic>u</italic> is the sum of labels of all arcs entering <italic>u</italic> minus the sum of labels of all arcs leaving <italic>u</italic>. <xref ref-type="bibr" rid="j_auom-2018-0039_ref_003_w2aab3b7b9b1b6b1ab1ab3Aa">Hefetz, Mütze, and Schwartz [3]</xref> conjectured that every connected graph admits an antimagic orientation, where an <italic>antimagic orientation</italic> of a graph <italic>G</italic> is an orientation of <italic>G</italic> which has an antimagic labeling. We use a constructive technique to prove that caterpillars, a well-known subclass of trees, have antimagic orientations.</p></abstract>

An antimagic labeling of a directed graph D with m arcs is a bijection from the set of arcs of D to {1, …, m} such that all oriented vertex sums of vertices in D are pairwise distinct, where the oriented vertex sum of a vertex u is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Hefetz, Mütze, and Schwartz [3] conjectured that every connected graph admits an antimagic orientation, where an antimagic orientation of a graph G is an orientation of G which has an antimagic labeling. We use a constructive technique to prove that caterpillars, a well-known subclass of trees, have antimagic orientations.

Caterpillars Have Antimagic Orientations

Universitat Politècnica de Catalunya - BarcelonaTech

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Caterpillars Have Antimagic Orientations"}

An antimagic labeling of a directed graph D with m arcs is a bijection from the set of arcs of D to {1, …, m} such that all oriented vertex sums of vertices in...

Caterpillars Have Antimagic Orientations

Published Online: Dec 31, 2018

Page range: 171 - 180

Received: Sep 05, 2017

Accepted: Oct 31, 2017

DOI: https://doi.org/10.2478/auom-2018-0039

Keywords
Caterpillar, Antimagic labeling, Antimagic orientation

© 2018 Antoni Lozano, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Caterpillars Have Antimagic Orientations

Published Online: Dec 31, 2018

Page range: 171 - 180

Received: Sep 05, 2017

Accepted: Oct 31, 2017

DOI: https://doi.org/10.2478/auom-2018-0039

KeywordsCaterpillar, Antimagic labeling, Antimagic orientation

© 2018 Antoni Lozano, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Caterpillar, Antimagic labeling, Antimagic orientation