A note on the intersection graph of the k-ideals of a semiring

Let R be a commutative semiring with identity. The intersection graph GS(R) is defined to be the undirected simple graph whose vertices are non-trivial k-ideals of R and two distinct vertices are adjacent if and only if the corresponding k-ideals of (R) have nonzero intersection. We investigate the interplay between the semiring-theoretic properties of (R) and the graph-theoretic properties of GS(R) . We determine the diameter and the girth of GS(R)