Geodesic
On graph associated to co-ideals of commutative semirings
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 293-305 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph $\Omega(R)$ whose vertices are all elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if the product of the co-ideals generated by $x$ and $y$ is $R$. Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph $\Gamma(R)$ and $\Omega(R)$.
Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph $\Omega(R)$ whose vertices are all elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if the product of the co-ideals generated by $x$ and $y$ is $R$. Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph $\Gamma(R)$ and $\Omega(R)$.
DOI : 10.14712/1213-7243.2015.219
Classification : 05C75, 16Y60
Keywords: semiring; co-ideal; maximal co-ideal 
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Talebi, Yahya; Darzi, Atefeh. On graph associated to co-ideals of commutative semirings. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 293-305. doi: 10.14712/1213-7243.2015.219

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