<i>D</i>-Magic Oriented Graphs
In this paper, we define <i>D</i>-magic labelings for oriented graphs where <i>D</i> is a distance set. In particular, we label the vertices of the graph with distinct integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2261 |
| _version_ | 1797500346696728576 |
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| author | Alison Marr Rinovia Simanjuntak |
| author_facet | Alison Marr Rinovia Simanjuntak |
| author_sort | Alison Marr |
| collection | DOAJ |
| description | In this paper, we define <i>D</i>-magic labelings for oriented graphs where <i>D</i> is a distance set. In particular, we label the vertices of the graph with distinct integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>}</mo></mrow></semantics></math></inline-formula> in such a way that the sum of all the vertex labels that are a distance in <i>D</i> away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of <i>D</i>-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of <i>D</i>-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of <i>D</i>-magic labelings. |
| first_indexed | 2024-03-10T03:00:36Z |
| format | Article |
| id | doaj.art-14224147886f4d3aa8cb853f6d96a808 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:00:36Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-14224147886f4d3aa8cb853f6d96a8082023-11-23T10:44:28ZengMDPI AGSymmetry2073-89942021-11-011312226110.3390/sym13122261<i>D</i>-Magic Oriented GraphsAlison Marr0Rinovia Simanjuntak1Department of Mathematics and Computer Science, Southwestern University, Georgetown, TX 78626, USACombinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, IndonesiaIn this paper, we define <i>D</i>-magic labelings for oriented graphs where <i>D</i> is a distance set. In particular, we label the vertices of the graph with distinct integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>}</mo></mrow></semantics></math></inline-formula> in such a way that the sum of all the vertex labels that are a distance in <i>D</i> away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of <i>D</i>-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of <i>D</i>-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of <i>D</i>-magic labelings.https://www.mdpi.com/2073-8994/13/12/2261oriented graphsdigraph labelingdistance magic labeling<i>D</i>-magic labeling |
| spellingShingle | Alison Marr Rinovia Simanjuntak <i>D</i>-Magic Oriented Graphs Symmetry oriented graphs digraph labeling distance magic labeling <i>D</i>-magic labeling |
| title | <i>D</i>-Magic Oriented Graphs |
| title_full | <i>D</i>-Magic Oriented Graphs |
| title_fullStr | <i>D</i>-Magic Oriented Graphs |
| title_full_unstemmed | <i>D</i>-Magic Oriented Graphs |
| title_short | <i>D</i>-Magic Oriented Graphs |
| title_sort | i d i magic oriented graphs |
| topic | oriented graphs digraph labeling distance magic labeling <i>D</i>-magic labeling |
| url | https://www.mdpi.com/2073-8994/13/12/2261 |
| work_keys_str_mv | AT alisonmarr idimagicorientedgraphs AT rinoviasimanjuntak idimagicorientedgraphs |