remarks on the zero-set intersection graph

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 $fg=0.$