Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 10 4 2025 12 01 Complete solutions on local antimagic chromatic number of three families of disconnected graphs 973 988 14722 10.22049/cco.2024.29032.1818 EN Tsz Lung Chan Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China Gee-Choon Lau College of Computing, Informatics & Mathematics, Universiti Teknologi MARA, Johor Branch, Segamat Campus, 85000 Malaysia Wai Chee Shiu Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China Journal Article 2023 10 05 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. https://comb-opt.azaruniv.ac.ir/article_14722_484086a5c1b730e5028d6b0a64ec958a.pdf