Co-maximal signed graphs of commutative rings
Authors : Deepa Sinha, Anita Kumari Rao
Pages : 1203-1220
View : 9 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let $ \Gamma(R)$ be a graph with element of $R$ (finite commutative ring with unity) as vertices, where two vertices $a$ and $b$ are adjacent if and only if $Ra+Rb = R$. In this paper, we characterize the rings for which a co-maximal meet signed graph $ \Gamma_{\Sigma}(R)$, a co-maximal join signed graph $ \Gamma_{\Sigma}^{\vee}(R)$, a co-maximal ring sum signed graph $ \Gamma_{\Sigma}^{\oplus}(R)$, their negation signed graphs $ \eta(\Gamma_{\Sigma}(R))$, $ \eta(\Gamma_{\Sigma}^{\vee}(R))$, $ \eta(\Gamma_{\Sigma}^{\oplus}(R))$ respectively and their line signed graphs are balanced, clusterable, and sign-compatible.Keywords : Finite commutative ring, maximal ideal, co-maximal graph, balanced signed graph, co-maximal meet signed graph, co-maximal join signed graph, co-maximal ring sum signed graph