A graph associated to a commutative semiring

Let R be a commutative finite semiring with nonzero identity and H an arbitrary multiplicatively closed subset . The generalized identity-summand graph of is the (simple) G ( ) GH(R) all elements as vertices, two distinct vertices x y are adjacent if only + ∈ x+y∈H In this paper, we study some basic properties Moreover, characterize planarity, chromatic number, clique number independence