Turkish Journal of Mathematics
DOI
10.3906/mat-1704-20
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
First Page
1203
Last Page
1220
Recommended Citation
SINHA, DEEPA and RAO, ANITA KUMARI
(2018)
"Co-maximal signed graphs of commutative rings,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 36.
https://doi.org/10.3906/mat-1704-20
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/36
