Abstract:
This dissertation deals with the algebraic invariants such as depth and dimension as
well as geometric invariant Stanley depth of some particular classes of graphs. Earlier,
we have some general bounds for these invariants. The present thesis is primarily
concerned with the value of depth and Stanley depth of edge ideals and their quotient
rings (cyclic modules) related to some classes of graphs. In some cases we have an
exact value, otherwise, we give very sharp bounds. In the end, we obtain a very strong
lower bound for the dimension of the quotient rings of the edge ideals associated with
these graphs. our results are general in nature, i.e., they hold for any non-negative
integer. Also, we examine conjecture of Herzog and question of Rauf.
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