Local distance antimagic chromatic number for the union of star and double star graphs
UDC 519.17 Let $G=(V,E)$ be a graph on $p$ vertices with no isolated vertices. A bijection $f$ from $V$ to $ \{1,2,3,\ldots ,p\}$ is called a local distance antimagic labeling if, for any two adjacent vertices $u$ and $v,$ we receive distinct weights (colors), where a...
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7075 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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| author | Priyadharshini, V. Nalliah, M. Priyadharshini, V. Nalliah, M. |
| author_facet | Priyadharshini, V. Nalliah, M. Priyadharshini, V. Nalliah, M. |
| author_sort | Priyadharshini, V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
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| datestamp_date | 2023-05-30T15:41:15Z |
| description |
UDC 519.17
Let $G=(V,E)$ be a graph on $p$ vertices with no isolated vertices. A bijection $f$ from $V$ to $ \{1,2,3,\ldots ,p\}$ is called a local distance antimagic labeling if, for any two adjacent vertices $u$ and $v,$ we receive distinct weights (colors), where a vertex $x$  has the weight  $w(x)=\displaystyle\sum\nolimits_{v\epsilon N(x)} f(v).$ The local distance antimagic chromatic number $\chi_{lda}(G)$ is defined as the least number of colors used in any local distance antimagic labeling of $G.$ We determine the local distance antimagic chromatic number for the disjoint union of $t$ copies of stars and double stars. |
| doi_str_mv | 10.37863/umzh.v75i5.7075 |
| first_indexed | 2026-03-24T03:31:14Z |
| format | Article |
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| id | umjimathkievua-article-7075 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:14Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-70752023-05-30T15:41:15Z Local distance antimagic chromatic number for the union of star and double star graphs Local distance antimagic chromatic number for the union of star and double star graphs Priyadharshini, V. Nalliah, M. Priyadharshini, V. Nalliah, M. Distance antimagic graphs, local distance antimagic chromatic number, star and double star graphs. 05C78 05C15 UDC 519.17 Let $G=(V,E)$ be a graph on $p$ vertices with no isolated vertices. A bijection $f$ from $V$ to $ \{1,2,3,\ldots ,p\}$ is called a local distance antimagic labeling if, for any two adjacent vertices $u$ and $v,$ we receive distinct weights (colors), where a vertex $x$  has the weight  $w(x)=\displaystyle\sum\nolimits_{v\epsilon N(x)} f(v).$ The local distance antimagic chromatic number $\chi_{lda}(G)$ is defined as the least number of colors used in any local distance antimagic labeling of $G.$ We determine the local distance antimagic chromatic number for the disjoint union of $t$ copies of stars and double stars. УДК 519.17 Антимагічне хроматичне число локальної відстані  для об’єднання зіркових і подвійних зіркових графів Нехай $G=(V,E)$ — граф на $p$ вершинах без ізольованих вершин. Бієкція $f$ з $V$ на $\{1,2,3,\ldots ,p\}$ називається локальним дистанційним антимагічним маркуванням, якщо для будь-яких двох суміжних вершин $u$ і $v$ отримано різні ваги (кольори), де вершина $x$ має вагу  $w(x)=\displaystyle\sum\nolimits_{v\epsilon N(x)} f(v).$ Антимагічне хроматичне число локальної відстані $\chi_{lda }(G)$ визначається, як найменша кількість кольорів, що використовуються в будь-якому локальному дистанційному антимагічному маркуванні $G.$ Отримано антимагічне хроматичне число локальної відстані для  об’єднання $t$ копій зірок та подвійних зірок, що не перетинаються. Institute of Mathematics, NAS of Ukraine 2023-05-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7075 10.37863/umzh.v75i5.7075 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 5 (2023); 669 - 682 Український математичний журнал; Том 75 № 5 (2023); 669 - 682 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7075/9773 Copyright (c) 2023 Priyadharshini V, Nalliah M |
| spellingShingle | Priyadharshini, V. Nalliah, M. Priyadharshini, V. Nalliah, M. Local distance antimagic chromatic number for the union of star and double star graphs |
| title | Local distance antimagic chromatic number for the union of star and double star graphs |
| title_alt | Local distance antimagic chromatic number for the union of star and double star graphs |
| title_full | Local distance antimagic chromatic number for the union of star and double star graphs |
| title_fullStr | Local distance antimagic chromatic number for the union of star and double star graphs |
| title_full_unstemmed | Local distance antimagic chromatic number for the union of star and double star graphs |
| title_short | Local distance antimagic chromatic number for the union of star and double star graphs |
| title_sort | local distance antimagic chromatic number for the union of star and double star graphs |
| topic_facet | Distance antimagic graphs local distance antimagic chromatic number star and double star graphs. 05C78 05C15 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7075 |
| work_keys_str_mv | AT priyadharshiniv localdistanceantimagicchromaticnumberfortheunionofstaranddoublestargraphs AT nalliahm localdistanceantimagicchromaticnumberfortheunionofstaranddoublestargraphs AT priyadharshiniv localdistanceantimagicchromaticnumberfortheunionofstaranddoublestargraphs AT nalliahm localdistanceantimagicchromaticnumberfortheunionofstaranddoublestargraphs |