Geodesic
A co-ideal based identity-summand graph of a commutative semiring
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 269-285.

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Let $I$ be a strong co-ideal of a commutative semiring $R$ with identity. Let $\Gamma_{I} (R)$ be a graph with the set of vertices $S_{I} (R) = \{x \in R\setminus I: x + y \in I$ for some $y \in R \setminus I\}$, where two distinct vertices $x$ and $y$ are adjacent if and only if $x + y \in I$. We look at the diameter and girth of this graph. Also we discuss when $\Gamma_{I} (R)$ is bipartite. Moreover, studies are done on the planarity, clique, and chromatic number of this graph. Examples illustrating the results are presented.
DOI : 10.14712/1213-7243.2015.124
Classification : 05C62, 16Y60
Keywords: strong co-ideal; $Q$-strong co-ideal; identity-summand element; identity-summand graph; co-ideal based 
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Atani, S. Ebrahimi; Hesari, S. Dolati Pish; Khoramdel, M. A co-ideal based identity-summand graph of a commutative semiring. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 269-285. doi : 10.14712/1213-7243.2015.124. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.124/

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