[1]Department of Mathematicsf University of Exlucation, Lahore, Pakistan;
[1]Department of Mathematicsf University of Exlucation, Lahore, Pakistan;
[2]University of Management and Technology, Lahore, Pakistan;
[3]Department of Mathematics, University of Education, Lahore, Pakistan;
[4]Department of Mathematics, COMSATS University Islamabad Sahiwal Campus, Sahiwal, Pakistan;
[1]Department of Mathematicsf University of Exlucation, Lahore, Pakistan;
simplicial complexes; spanning trees; spanning simplicial complexes; f-vectors; Hilbert series; vertex covers;