A note on graphical representation of rings
Main result: Let \(R\) be a commutative ring with identity. \(R\) may be regarded as a graph with elements of \(R\) as vertices. Two distinct vertices \(x\) and \(y\) are said to be adjacent if and only if \(Rx+ Ry= R\). Then the chromatic number \(\chi(R)< \infty\) if and only if \(R\) is a finite ring. In this case \(\chi(R)=\text{clique } R= t+ \ell\), where \(t\) and \(\ell\) respectively denote the number of maximal ideals of \(R\) and the number of units of \(R\).
scientific article; zbMATH DE number 802372