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Complete solutions on local antimagic chromatic number of three families of disconnected graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 13، دوره 10، شماره 4، اسفند 2025، صفحه 973-988 اصل مقاله (506.34 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29032.1818 | ||
| نویسندگان | ||
| Tsz Lung Chan1؛ Gee-Choon Lau* 2؛ Wai Chee Shiu3 | ||
| 1Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China | ||
| 2College of Computing, Informatics & Mathematics, Universiti Teknologi MARA, Johor Branch, Segamat Campus, 85000 Malaysia | ||
| 3Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China | ||
| چکیده | ||
| An edge labeling of a graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all the edges incident to $x$. The local antimagic chromatic number of $G$, denoted by $\chi_{la}(G)$, is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G$. In this paper, we study local antimagic labeling of disjoint unions of stars, paths and cycles whose components need not be identical. Consequently, we completely determined the local antimagic chromatic numbers of disjoint union of 2 stars, paths, and 2-regular graphs with at most one odd order component respectively. | ||
| کلیدواژه‌ها | ||
| Local antimagic labeling؛ local antimagic chromatic number؛ disconnected graphs | ||
| مراجع | ||
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