## On the connectedness of $$f$$-simplicial complexes.(English)Zbl 1362.13029

The authors in this paper introduce the notion of a $$f$$-simplicial complex which generalises the term $$f$$-graph defined in [G. Q. Abbasi et al., Algebra Colloq. 19, 921–926 (2012; Zbl 1294.13031)]. They mainly interested in studying the connectedness and disconnectedness property. They show that a pure $$f$$-simplicial complex of dimension $$\geq 2$$ is connected. In their next result, they give a complete characterisation of disconnected $$f$$-graphs.

### MSC:

 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes 13C14 Cohen-Macaulay modules

Zbl 1294.13031
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### References:

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