Abstract:
In the field of abstract algebra module is an algebraic structure and Stanley depth
and depth are its geometric and algebraic invariants, respectively. This dissertation is
mainly concerned with the Stanley depth and depth of residue class rings of some trees
and unicyclic graphs. The exact values of Stanley depth and depth have been computed
earlier for perfect ('1)-ary trees, and these values are used while computing Stanley
depth and depth in the main results of this dissertation. The results computed in this
research are of exact values of Stanley depth and depth except for Stanley depth of one
special case of unicyclic graph for which tight bound is given. It is observed that the
results are good and satisfactory, since they cover the graphs with three parameters
which can be assigned any positive integer values, and this is not an easy task to handle
since there is no smooth and easy method devised for such computations.
