ZERO-SET INTERSECTION GRAPH ON C+(X)

Abstract

For any Tychonoff space X we have introduced the zero-set intersection 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.