Depth and Stanley Depth of Residue Class Rings Associated to Edge Ideals of Some Classes of Trees and Unicyclic Graphs

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 ('ð€€€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.