The Graceful Coalescence of Alpha Cycles
The standard coalescence of two graphs is extended, allowing to identify two isomorphic subgraphs instead of a single vertex. It is proven here that any succesive coalescence of cycles of size $n$, where $n$ is divisible by four, results in an $\alpha$-graph, that is, the most restrictive kind of gr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2019-06-01
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| Series: | Communications in Advanced Mathematical Sciences |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/745297 |
| _version_ | 1797294151832698880 |
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| author | Christian Barrientos Sarah Minion |
| author_facet | Christian Barrientos Sarah Minion |
| author_sort | Christian Barrientos |
| collection | DOAJ |
| description | The standard coalescence of two graphs is extended, allowing to identify two isomorphic subgraphs instead of a single vertex. It is proven here that any succesive coalescence of cycles of size $n$, where $n$ is divisible by four, results in an $\alpha$-graph, that is, the most restrictive kind of graceful graph, when the subgraphs identified are paths of sizes not exceeding $\frac{n}{2}$. Using the coalescence and another similar technique, it is proven that some subdivisions of the ladder $L_n = P_2 \times P_n$ also admit an $\alpha$-labeling, extending and generalizing the existing results for this type of subdivided graphs. |
| first_indexed | 2024-03-07T21:26:07Z |
| format | Article |
| id | doaj.art-b2faa03b44af4d63b7891ee91acea119 |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:26:07Z |
| publishDate | 2019-06-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-b2faa03b44af4d63b7891ee91acea1192024-02-27T04:36:37ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012019-06-012211412010.33434/cams.5054851225The Graceful Coalescence of Alpha CyclesChristian Barrientos0Sarah Minion1Valencia CollegeValencia CollegeThe standard coalescence of two graphs is extended, allowing to identify two isomorphic subgraphs instead of a single vertex. It is proven here that any succesive coalescence of cycles of size $n$, where $n$ is divisible by four, results in an $\alpha$-graph, that is, the most restrictive kind of graceful graph, when the subgraphs identified are paths of sizes not exceeding $\frac{n}{2}$. Using the coalescence and another similar technique, it is proven that some subdivisions of the ladder $L_n = P_2 \times P_n$ also admit an $\alpha$-labeling, extending and generalizing the existing results for this type of subdivided graphs.https://dergipark.org.tr/tr/download/article-file/745297coalescence$\alpha$-labelinggraceful labelingladder |
| spellingShingle | Christian Barrientos Sarah Minion The Graceful Coalescence of Alpha Cycles Communications in Advanced Mathematical Sciences coalescence $\alpha$-labeling graceful labeling ladder |
| title | The Graceful Coalescence of Alpha Cycles |
| title_full | The Graceful Coalescence of Alpha Cycles |
| title_fullStr | The Graceful Coalescence of Alpha Cycles |
| title_full_unstemmed | The Graceful Coalescence of Alpha Cycles |
| title_short | The Graceful Coalescence of Alpha Cycles |
| title_sort | graceful coalescence of alpha cycles |
| topic | coalescence $\alpha$-labeling graceful labeling ladder |
| url | https://dergipark.org.tr/tr/download/article-file/745297 |
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