We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let $G$ be a graph of order $p$ without isolated vertices.
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Temel Bulgular & Veri:A bijection $f: V \to \{1,2,3,\dots,p\}$ is called a local distance antimagic labeling, if $w_f(u)\ne w_f(v)$ for every edge $uv$ of $G$, where $w_f(u)=\sum_{x\epsilon N(u)} {f(x)}$.
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Sonuç & Katkı:We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:local distance antimagic chromatic number · join product · cycle
Abstract
Let $G$ be a graph of order $p$ without isolated vertices. A bijection $f: V \to \{1,2,3,\dots,p\}$ is called a local distance antimagic labeling, if $w_f(u)\ne w_f(v)$ for every edge $uv$ of $G$, where $w_f(u)=\sum_{x\epsilon N(u)} {f(x)}$. The local distance antimagic chromatic number $\chi_{lda}(G)$ is defined to be the minimum number of colors taken over all colorings of $G$ induced by local distance antimagic labelings of $G$. In this paper, we determined the local distance antimagic chromatic number of some cycles, paths, disjoint union of 3-paths. We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.
Shiu, W., Lau, G., M, N. (2024). Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 3. https://doi.org/10.15672/hujms.1266085
S. Arumugam, D. Froncek, and N. Kamatchi, Distance magic graphs–A survey, J. Indones. Math. Soc. Special Edition, 1126, 2011.
S. Arumugam and N. Kamatchi, On $(a, d)$-distance antimagic graphs, Australas. J. Combin. 54, 279–287, 2012.
S. Arumugam, K. Premalatha, M. Bača and A. Semaničová-Fecňovčíková, Local antimagic vertex coloring of a graph, Graphs Combin. 33, 275–285, 2017.
J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, New York, MacMillan, 1976.
J. Bensmail, M. Senhaji and K.S. Lyngsie, On a combination of the 1-2-3 conjecture and the antimagic labelling conjecture, Discrete Math. Theor. Comput. Sci. 19 (1), 2017.