Quasi f-Simplicial Complexes and Quasi f-Graphs

TL;DR

This paper introduces quasi f-simplicial complexes and quasi f-graphs, expanding the concept of f-ideals, and provides characterizations, connectedness criteria, and Cohen-Macaulay constructions for these structures.

Contribution

It generalizes the notion of f-ideals to quasi f-ideals, introduces quasi f-simplicial complexes and graphs, and offers characterizations and construction methods for Cohen-Macaulay cases.

Findings

Characterization of quasi f-graphs on n vertices

Complete solution for connectedness of quasi f-simplicial complexes

Method for constructing Cohen-Macaulay quasi f-graphs

Abstract

The notion of $f$-ideal is recent and has so far been studied in several papers. In \cite{qfi}, the idea of $f$-ideal is generalized to quasi $f$-ideals, which is much larger class than the class of $f$-ideals. In this paper, we introduce the concept of quasi $f$-simplicial complex and quasi $f$-graph. We give a characterization of quasi $f$-graphs on $n$ vertices. A complete solution of connectedness of quasi $f$-simplicial complexes is described. We have also shown a method of constructing Cohen-Macaulay quasi $f$-graphs.