What question did this study set out to answer?

To determine the chromatic number of connected Cayley graphs based on their Heuberger matrices, focusing on low-dimensional cases.

Chromatic numbers of Cayley graphs of abelian groups: cases of small dimension and rank

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To determine the chromatic number of connected Cayley graphs based on their Heuberger matrices, focusing on low-dimensional cases.
Analyzed Cayley graphs represented by Heuberger matrices for specific conditions on dimension and rank.
Established colorability conditions for graphs with dimension 1 and rank 1, as well as dimension ≤ 3 and rank ≤ 2.
Defined specific graph structures like diamond lanyards and C13 (1, 5) for colorability determination.
Graphs are 4-colorable if they do not contain a 5-clique; conversely, they are 3-colorable if they lack a diamond lanyard or C13 (1, 5).
Numerical conditions fully characterize chromatic numbers for specified dimensions and ranks.
Improved upper bounds for optimal colorings of 6-valent integer distance graphs are derived as a consequence of the findings.

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This randomized trial evaluates chromatic numbers in Cayley graphs, suggesting key conditions for colorability in small dimensions and ranks.

Cervantes et al. (2026) studied this question.

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This randomized trial evaluates chromatic numbers in Cayley graphs, suggesting key conditions for colorability in small dimensions and ranks.