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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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
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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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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| DOI: | 10.37863/umzh.v75i5.7075 |