Geodesic
On Local Antimagic Chromatic Number of Cycle-Related Join Graphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 133-152 Cet article a éte moissonné depuis la source Library of Science

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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 : E → 1, . . ., |E| such that for any pair of adjacent vertices x and y, f+(x) ≠ f+(y), where the induced vertex label f+(x) = Σf(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χla(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, several sufficient conditions for χla(H) ≤ χla(G) are obtained, where H is obtained from G with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs.
Keywords: local antimagic labeling, local antimagic chromatic number, cycle, join graphs 
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Lau, Gee-Choon; Shiu, Wai-Chee; Ng, Ho-Kuen. On Local Antimagic Chromatic Number of Cycle-Related Join Graphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 133-152. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a8/

[1] S. Arumugam, K. Premalatha, M. Bača and A. Semaničová-Feňovčíková, Local antimagic vertex coloring of a graph, Graphs Combin. 33 (2017) 275–285. doi: 10.1007/s00373-017-1758-7

[2] J. Bensmail, M. Senhaji and K. Szabo Lyngsie, On a combination of the 1-2-3 conjecture and the antimagic labelling conjecture, Discrete Math. Theor. Comput. Sci. 19 (2017) #21.

[3] F.S. Chai, A. Das and C. Midha, Construction of magic rectangles of odd order, Australas. J. Combin. 55 (2013) 131–144.

[4] G.C. Lau, H.K. Ng and W.C. Shiu, Affirmative solutions on local antimagic chromatic number (2018). arXiv:1805.02886

[5] J. Haslegrave, Proof of a local antimagic conjecture (2017). arXiv:1705.09957v1.

[6] J.P. De Los Reyes, A. Das and C.K. Midha, A matrix approach to construct magic rectangles of even order, Australas. J. Combin. 40 (2008) 293–300.

[7] X. Yu, J. Hu, D. Yang, J. Wu and G. Wang, Local antimagic labeling of graphs, Appl. Math. Comput. 322 (2018) 30–39. doi: 10.1016/j.amc.2017.10.008