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 ۰ is a cut vertex of \Gamma(C(X)) iff |X|=۲, and for a first countable space X, \Gamma(C(X)) is chordal iff |X|=۲ \ or\ |X|=۳. 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=۰.

کلیدواژه ها:

line graph ، Triangulated ، Chordal ، Complemented ، Ring of real-valued continuous functions