Abstract:
In this thesis, we discuss some fundamental concept of Abstract Algebra like rings
and modules. Furthermore, we discuss the Algebraic invariants Stanley depth and
depth. We also discuss some known results related to these invariants. Afterwards, we
compute the exact value of Stanley depth and depth of the quotient rings of the edge
ideals associated with ϱ-fold bristled graph of ladder graph, circular ladder graph, and
strong product of two graphs when both graphs are paths or when one of them is a
cycle and other is a path. We also proved that both these invariants have the same
values for all the classes, we considered.
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