THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS Atani, Shahabaddin Ebrahimi; Hesari, Saboura Dolati Pish; Khoramdel, Mehdi;
An element r of a commutative semiring R with identity is said to be identity-summand if there exists such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by . It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph are studied.