2024/10/23 by Gee-Choon Lau, Lau, Gee-Choon, Wai Chee Shiu +1
Computer Science · Mathematics · #05C69 #05C78 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2410.17674
openalex publication_date 2024/10/23 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28
It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we proved that the join of 1-regular graph and a null graph has local antimagic chromatic number is 3. Consequently, we also obtained many families of (possibly disconnected or regular) bipartite and tripartite graph with local antimagic chromatic number 3.