Remarks on the zero-set intersection graph

Document Type : Research Paper

Authors

Department of Mathematics, North-Eastern Hill University, Shillong, India

Abstract

In this paper, we study the zero-set intersection graph ($\Gamma(C(X))$) and its line graph ($L(\Gamma(C(X)))$). We showed that $0$ is a cut vertex of $\Gamma(C(X))$ iff $|X|=2$, and for a first countable space $X$, $\Gamma(C(X))$ is chordal iff $|X|=2 \ or\ |X|=3.$ We stated some conditions for a maximal clique to be a maximal ideal. We obtained that two (first countable/real compact) topological spaces $X$ and $Y$ are homeomorphic iff $L(\Gamma(C(X)))$ is graph isomorphic to $L(\Gamma(C(Y)))$ iff $C(X)$ is isomorphic to $C(Y).$ We showed that $\{f,g\}$ is a dominating set of $\Gamma(C(X))$ iff $fg=0.$

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References

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Journal of Algebra and Related Topics
Volume 13, Issue 2
December 2025
Pages 99-108

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