Abstract:
This dissertation aims to find a geometric invariant as well as the algebraic invariant
of the graphs. The desire is to obtain required invariants such as depth and Stanley
depth by using edge ideals as module over a polynomial ring as well as the quotient of
polynomial ring by monomial ideals. For this purpose, square free monomial ideals are
sought and critically reviewed.
In this thesis, we find the exact values of depth and Stanley depth of quotient of the
polynomial ring by the edge ideal associated with a Tadpole graph. It is shown that
the values of these two invariants coincide. We also find the tight bounds for Sdepth
and Depth of quotient of the polynomial ring by the edge ideal corresponding to square
of a Tadpole graph.
