On additive vertex labelings
<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weig...
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| Format: | Article |
| Language: | English |
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InaCombS; Universitas Jember; dan Universitas Indonesia
2020-06-01
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| Series: | Indonesian Journal of Combinatorics |
| Subjects: | |
| Online Access: | http://www.ijc.or.id/index.php/ijc/article/view/121 |
| _version_ | 1828487525882134528 |
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| author | Christian Barrientos |
| author_facet | Christian Barrientos |
| author_sort | Christian Barrientos |
| collection | DOAJ |
| description | <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weight of each edge is obtained by adding the labels of its end-vertices. In this work we study one of these functions, called harmonious labeling. We calculate the number of non-isomorphic harmoniously labeled graphs with <em>n</em> edges and at most </span><span>n </span><span>vertices. We present harmonious labelings for some families of graphs that include certain unicyclic graphs obtained via the corona product. In addition, we prove that all <em>n</em>-cell snake polyiamonds are harmonious; this type of graph is obtained via edge amalgamation of n copies of the cycle <em>C</em><sub>3</sub> in such a way that each copy of this cycle shares at most two edges with other copies. Moreover, we use the edge-switching technique on the cycle <em>C</em><sub>4<em>t</em> </sub>to generate unicyclic graphs with another type of additive vertex labeling, called strongly felicitous, which has a solid bond with the harmonious labeling.</span></p></div></div></div> |
| first_indexed | 2024-12-11T09:52:15Z |
| format | Article |
| id | doaj.art-3e94f15c3e03486eb2347885e7bfbb59 |
| institution | Directory Open Access Journal |
| issn | 2541-2205 |
| language | English |
| last_indexed | 2024-12-11T09:52:15Z |
| publishDate | 2020-06-01 |
| publisher | InaCombS; Universitas Jember; dan Universitas Indonesia |
| record_format | Article |
| series | Indonesian Journal of Combinatorics |
| spelling | doaj.art-3e94f15c3e03486eb2347885e7bfbb592022-12-22T01:12:22ZengInaCombS; Universitas Jember; dan Universitas IndonesiaIndonesian Journal of Combinatorics2541-22052020-06-0141345210.19184/ijc.2020.4.1.540On additive vertex labelingsChristian Barrientos0Valencia College<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weight of each edge is obtained by adding the labels of its end-vertices. In this work we study one of these functions, called harmonious labeling. We calculate the number of non-isomorphic harmoniously labeled graphs with <em>n</em> edges and at most </span><span>n </span><span>vertices. We present harmonious labelings for some families of graphs that include certain unicyclic graphs obtained via the corona product. In addition, we prove that all <em>n</em>-cell snake polyiamonds are harmonious; this type of graph is obtained via edge amalgamation of n copies of the cycle <em>C</em><sub>3</sub> in such a way that each copy of this cycle shares at most two edges with other copies. Moreover, we use the edge-switching technique on the cycle <em>C</em><sub>4<em>t</em> </sub>to generate unicyclic graphs with another type of additive vertex labeling, called strongly felicitous, which has a solid bond with the harmonious labeling.</span></p></div></div></div>http://www.ijc.or.id/index.php/ijc/article/view/121additive vertex labelingharmoniouscorona productunicyclicpolyiamonds |
| spellingShingle | Christian Barrientos On additive vertex labelings Indonesian Journal of Combinatorics additive vertex labeling harmonious corona product unicyclic polyiamonds |
| title | On additive vertex labelings |
| title_full | On additive vertex labelings |
| title_fullStr | On additive vertex labelings |
| title_full_unstemmed | On additive vertex labelings |
| title_short | On additive vertex labelings |
| title_sort | on additive vertex labelings |
| topic | additive vertex labeling harmonious corona product unicyclic polyiamonds |
| url | http://www.ijc.or.id/index.php/ijc/article/view/121 |
| work_keys_str_mv | AT christianbarrientos onadditivevertexlabelings |