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On local antimagic chromatic numbers of the join of two special families of graphs
- Publication Year :
- 2024
-
Abstract
- It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we use matrices of size $(2m+1) \times (2k+1)$ to completely determine the local antimagic chromatic number of the join of null graphs, $O_m, m\ge 1,$ and 1-regular graphs of odd components, $(2k+1)P_2$, $k\ge 1$. Consequently, we obtained infinitely many (possibly disconnected or regular) tripartite graphs with local antimagic chromatic number 3.<br />Comment: 15 pages, 8 figures
- Subjects :
- Mathematics - Combinatorics
05C78, 05C69
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.04942
- Document Type :
- Working Paper