Let G be a finite simple graph. As a generalization of the edge ideal of G, the t-clique ideal of G denoted by KtðGÞ is defined as a monomial ideal generated by the monomials whose supports are t-cliques of G. In this paper, we study some families of t-clique ideals which their Stanley–Reisner simplicial complexes have properties such as shellability and vertex decomposability. Also, we investigate some t-clique ideals with linear resolutions.
