Abstract Two colourings of a graph are orthogonal if they have the property that when two vertices are coloured with the same colour in one colouring, then those vertices receive distinct colours in the other colouring. In this paper, orthogonal colourings of Cayley graphs are discussed. Firstly, the orthogonal chromatic number of cycle graphs are completely determined. Secondly, the orthogonal chromatic number of certain circulant graphs is explored. Lastly, orthogonal colourings of product graphs and Hamming graphs are studied.

中文翻译：

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Cayley 图的正交着色

摘要 一个图的两种颜色是正交的，如果它们具有这样的性质：当两个顶点在一种颜色中被着色为相同的颜色时，这些顶点在另一种颜色中会收到不同的颜色。本文讨论了凯莱图的正交着色。首先，完全确定循环图的正交色数。其次，探索了某些循环图的正交色数。最后，研究了乘积图和汉明图的正交着色。