On local antimagic chromatic numbers of the join of two special families of graphs

Fuente: arXiv
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Autori principali: Lau, Gee-Choon, Shiu, Wai Chee
Natura: Preprint
Pubblicazione: 2024
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author Lau, Gee-Choon
Shiu, Wai Chee
author_facet Lau, Gee-Choon
Shiu, Wai Chee
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_04942
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On local antimagic chromatic numbers of the join of two special families of graphs
Lau, Gee-Choon
Shiu, Wai Chee
Combinatorics
05C78, 05C69
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.
title On local antimagic chromatic numbers of the join of two special families of graphs
topic Combinatorics
05C78, 05C69
url https://arxiv.org/abs/2408.04942