Alpha graphs with different pendent paths
| Main Author: | Barrientos, Christian; Department of Mathematics Valencia College |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2020
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1036 https://www.ejgta.org/index.php/ejgta/article/view/1036/pdf_143 |
| ctrlnum |
article-1036 |
|---|---|
| fullrecord |
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<dc schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><title lang="en-US">Alpha graphs with different pendent paths</title><creator>Barrientos, Christian; Department of Mathematics
Valencia College</creator><subject lang="en-US">α-labeling, graceful graph, unicyclic graph</subject><subject lang="en-US">05C78, 05C30</subject><description lang="en-US">Graceful labelings are an effective tool to find cyclic decompositions of complete graphs and complete bipartite graphs. The strongest kind of graceful labeling, the α-labeling, is in the center of the research field of graph labelings, the existence of an α-labeling of a graph implies the existence of several, apparently non-related, other labelings for that graph. Furthermore, graphs with α-labelings can be combined to form new graphs that also admit this type of labeling. The standard way to combine these graphs is to identify every vertex of a base graph with a vertex of another graph. These methods have in common that all the graphs involved, except perhaps the base, have the same size. In this work, we do something different, we prove the existence of an α-labeling of a tree obtained by attaching paths of different lengths to the vertices of a base path, in such a way that the lengths of the pendent paths form an arithmetic sequence with difference one, where consecutive vertices of the base path are identified with paths which lengths are consecutive elements of the sequence. These α-trees are combined in several ways to generate new families of α-trees. We also prove that these trees can be used to create unicyclic graphs with an α-labeling. In addition, we show that the pendent paths can be substituted by equivalent α-trees to produce new α-trees, obtaining in this manner a quite robust category of α-trees.</description><publisher lang="en-US">GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB</publisher><contributor lang="en-US"/><date>2020-10-16</date><type>Journal:Article</type><type>Other:info:eu-repo/semantics/publishedVersion</type><type>Journal:Article</type><type>File:application/pdf</type><identifier>https://www.ejgta.org/index.php/ejgta/article/view/1036</identifier><identifier>10.5614/ejgta.2020.8.2.8</identifier><source lang="en-US">Electronic Journal of Graph Theory and Applications (EJGTA); Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications; 301 - 317</source><source>2338-2287</source><language>eng</language><relation>https://www.ejgta.org/index.php/ejgta/article/view/1036/pdf_143</relation><rights lang="en-US">Copyright (c) 2020 Electronic Journal of Graph Theory and Applications (EJGTA)</rights><recordID>article-1036</recordID></dc>
|
| language |
eng |
| format |
Journal:Article Journal Other:info:eu-repo/semantics/publishedVersion Other File:application/pdf File Journal:eJournal |
| author |
Barrientos, Christian; Department of Mathematics
Valencia College |
| title |
Alpha graphs with different pendent paths |
| publisher |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB |
| publishDate |
2020 |
| topic |
α-labeling graceful graph unicyclic graph 05C78 05C30 |
| url |
https://www.ejgta.org/index.php/ejgta/article/view/1036 https://www.ejgta.org/index.php/ejgta/article/view/1036/pdf_143 |
| contents |
Graceful labelings are an effective tool to find cyclic decompositions of complete graphs and complete bipartite graphs. The strongest kind of graceful labeling, the α-labeling, is in the center of the research field of graph labelings, the existence of an α-labeling of a graph implies the existence of several, apparently non-related, other labelings for that graph. Furthermore, graphs with α-labelings can be combined to form new graphs that also admit this type of labeling. The standard way to combine these graphs is to identify every vertex of a base graph with a vertex of another graph. These methods have in common that all the graphs involved, except perhaps the base, have the same size. In this work, we do something different, we prove the existence of an α-labeling of a tree obtained by attaching paths of different lengths to the vertices of a base path, in such a way that the lengths of the pendent paths form an arithmetic sequence with difference one, where consecutive vertices of the base path are identified with paths which lengths are consecutive elements of the sequence. These α-trees are combined in several ways to generate new families of α-trees. We also prove that these trees can be used to create unicyclic graphs with an α-labeling. In addition, we show that the pendent paths can be substituted by equivalent α-trees to produce new α-trees, obtaining in this manner a quite robust category of α-trees. |
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IOS276.article-1036 |
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Indonesian Combinatorial Society |
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93 |
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library:special library |
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Indonesian Combinatorial Society |
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72 |
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Electronic Journal of Graph Theory and Applications (EJGTA) |
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276 |
| subject_area |
Rekayasa Mathematics/Matematika Data Processing, Computer Science/Pemrosesan Data, Ilmu Komputer, Teknik Informatika Applied mathematics/Matematika Terapan |
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BANDUNG |
| province |
JAWA BARAT |
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2020-11-01T01:35:06Z |
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2023-04-22T16:36:53Z |
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1800700566557425664 |
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16.845257 |