On graphs with α- and <em>b</em>-edge consecutive edge magic labelings
<p>Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related. A graceful labeling of a bipartite graph is called an α-labeling if the smaller labels are assigned to vertices of th...
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| Format: | Article |
| Language: | English |
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InaCombS; Universitas Jember; dan Universitas Indonesia
2022-06-01
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| Series: | Indonesian Journal of Combinatorics |
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| Online Access: | http://www.ijc.or.id/index.php/ijc/article/view/171 |
| _version_ | 1828057137553604608 |
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| author | Christian Barrientos |
| author_facet | Christian Barrientos |
| author_sort | Christian Barrientos |
| collection | DOAJ |
| description | <p>Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related. A graceful labeling of a bipartite graph is called an α-labeling if the smaller labels are assigned to vertices of the same stable set. An edge-magic labeling of a graph of size <em>n</em> is said to be <em>b</em>-edge consecutive when its edges are labeled with the integers <em>b+1</em>, <em>b+2</em>, ..., <em>b+n</em>, for some 0 ≤ <em>b</em> ≤ <em>n</em>. In this work, we prove the existence of several <em>b</em> edge-magic labelings for any graph of order <em>m</em> and size <em>m-1</em> that admits an α-labeling. In addition, we determine the exact value of <em>b</em> induced by the α-labeling, as well as for its reverse, complementary, and reverse complementary labelings.</p> |
| first_indexed | 2024-04-10T21:07:48Z |
| format | Article |
| id | doaj.art-7c1ecd445c1745338b666656b695c8c5 |
| institution | Directory Open Access Journal |
| issn | 2541-2205 |
| language | English |
| last_indexed | 2024-04-10T21:07:48Z |
| publishDate | 2022-06-01 |
| publisher | InaCombS; Universitas Jember; dan Universitas Indonesia |
| record_format | Article |
| series | Indonesian Journal of Combinatorics |
| spelling | doaj.art-7c1ecd445c1745338b666656b695c8c52023-01-22T03:10:04ZengInaCombS; Universitas Jember; dan Universitas IndonesiaIndonesian Journal of Combinatorics2541-22052022-06-0161586510.19184/ijc.2022.6.1.472On graphs with α- and <em>b</em>-edge consecutive edge magic labelingsChristian Barrientos0Valencia College<p>Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related. A graceful labeling of a bipartite graph is called an α-labeling if the smaller labels are assigned to vertices of the same stable set. An edge-magic labeling of a graph of size <em>n</em> is said to be <em>b</em>-edge consecutive when its edges are labeled with the integers <em>b+1</em>, <em>b+2</em>, ..., <em>b+n</em>, for some 0 ≤ <em>b</em> ≤ <em>n</em>. In this work, we prove the existence of several <em>b</em> edge-magic labelings for any graph of order <em>m</em> and size <em>m-1</em> that admits an α-labeling. In addition, we determine the exact value of <em>b</em> induced by the α-labeling, as well as for its reverse, complementary, and reverse complementary labelings.</p>http://www.ijc.or.id/index.php/ijc/article/view/171α-labeling, edge-magic graph, b-edge consecutive |
| spellingShingle | Christian Barrientos On graphs with α- and <em>b</em>-edge consecutive edge magic labelings Indonesian Journal of Combinatorics α-labeling, edge-magic graph, b-edge consecutive |
| title | On graphs with α- and <em>b</em>-edge consecutive edge magic labelings |
| title_full | On graphs with α- and <em>b</em>-edge consecutive edge magic labelings |
| title_fullStr | On graphs with α- and <em>b</em>-edge consecutive edge magic labelings |
| title_full_unstemmed | On graphs with α- and <em>b</em>-edge consecutive edge magic labelings |
| title_short | On graphs with α- and <em>b</em>-edge consecutive edge magic labelings |
| title_sort | on graphs with 945 and em b em edge consecutive edge magic labelings |
| topic | α-labeling, edge-magic graph, b-edge consecutive |
| url | http://www.ijc.or.id/index.php/ijc/article/view/171 |
| work_keys_str_mv | AT christianbarrientos ongraphswith945andembemedgeconsecutiveedgemagiclabelings |