Geodesic
Complete characterization of bridge graphs with local antimagic chromatic number~$2$
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 375-396

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An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f\colon E \to\{1,\ldots ,|E|\}$ 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 characterize $s$-bridge graphs with local antimagic chromatic number $2$.
Keywords: local antimagic labeling, local antimagic chromatic number, $s$-bridge graphs 
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     title = {Complete characterization of bridge graphs with local antimagic chromatic number~$2$},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a4/}
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G.-Ch. Lau; W. Ch. Shiu; M. Ch. Nalliah; R. Zhang; K. Premalatha. Complete characterization of bridge graphs with local antimagic chromatic number~$2$. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 375-396. http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a4/