### Some properties of the maximal graph related to co-ideal of a commutative semiring

**Yahya Talebi, Atefeh Darzi**

**Abstract:**For a commutative semiring \(R\) with non-zero identity, the maximal graph of \(R\), denoted by \(MG(R)\), is the graph whose vertices are all elements of \(UM(R)\) with two distinct vertices joined by an edge when there is a maximal co-ideal that contains both of them. In this paper, we study some properties of maximal graph such as planarity, radius, splitting and domination number.