Zero-Set Intersection Graph On C+(X)

Abstract

For any Tychonoff space X we have introduced the zero-set in-tersection graph on Γ(C+(X)) and studied the graph properties in connection with the algebraic properties of the semiring C+(X). We have shown that for any two realcompact spaces X and Y the graph isomorphism between Γ(C+(X)) and Γ(C+(Y )), the semiring isomorphism between C+(X) and C+(Y ), the topological homeomorphism between X and Y, the ring isomorphism between C(X) and C(Y ) and the graph isomorphism between Γ(C(X)) and Γ(C(Y )) are equivalent.