On local antimagic chromatic number of the join of two special families of graphs | II

Null graphs (respectively, 1-regular graphs) are the only regular graphs with local antimagic chromatic number 1 (respectively, undefined). In this paper, we proved that the join of 1-regular graph and a null graph has local antimagic chromatic number 3. As a by-product, we also obtained many families of (possibly disconnected or regular) bipartite and tripartite graph with local antimagic chromatic number 3.

Publication Details

Journal
Utilitas Mathematica
Published
2025-09-27
DOI
https://doi.org/10.61091/um124-12
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
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On local antimagic chromatic number of the join of two special families of graphs | II

Utilitas Mathematica
Geochemistry and Geologic Mapping
article

On local antimagic chromatic number of the join of two special families of graphs | II

article en

Abstract

Null graphs (respectively, 1-regular graphs) are the only regular graphs with local antimagic chromatic number 1 (respectively, undefined). In this paper, we proved that the join of 1-regular graph and a null graph has local antimagic chromatic number 3. As a by-product, we also obtained many families of (possibly disconnected or regular) bipartite and tripartite graph with local antimagic chromatic number 3.

Utilitas MathematicaVol. 124
Openalex Percentile: Top 26%
Geochemistry and Geologic Mapping
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On local antimagic chromatic number of the join of two special families of graphs | II · Utilitas Mathematica (2025) | TGRS Research Map | TGRS