Shaveisi, F. (2017). The central vertices and radius of the regular graph of ideals. Transactions on Combinatorics, 6(4), 1-13. doi: 10.22108/toc.2017.21472

Farzad Shaveisi. "The central vertices and radius of the regular graph of ideals". Transactions on Combinatorics, 6, 4, 2017, 1-13. doi: 10.22108/toc.2017.21472

Shaveisi, F. (2017). 'The central vertices and radius of the regular graph of ideals', Transactions on Combinatorics, 6(4), pp. 1-13. doi: 10.22108/toc.2017.21472

Shaveisi, F. The central vertices and radius of the regular graph of ideals. Transactions on Combinatorics, 2017; 6(4): 1-13. doi: 10.22108/toc.2017.21472

The central vertices and radius of the regular graph of ideals

The regular graph of ideals of the commutative ring $R$, denoted by ${\Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is proved that the radius of $\Gamma_{reg}(R)$ equals $3$. The central vertices of $\Gamma_{reg}(R)$ are determined, too.

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