Examines the graph properties related to algebraic properties in Tychonoff spaces, suggesting connections between their structures.
For any Tychonoff space X we have introduced the zero-set intersection graph on ?(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, ?(C+(X)) is isomorphic to ?(C+(Y)) if and only if C+(X) is isomorphic to C+(Y) if and only if X is homeomorphic to Y if and only if C(X) is isomorphic to C(Y) if and only if ?(C(X)) is isomorphic to ?(C(Y)).
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Basu et al. (2025) studied this question.
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