Subspace inclusion graphs over residue class rings modulo prime power

Let Z_{p^s} denote the residue class ring modulo p^s, where p is a prime number and s is a positive integer. In this thesis, we introduce the subspace inclusion graph In(Z_{p^s}^n), which is a graph whose vertices are the non-trivial proper subspaces of Z_{p^s}^n (for n<= 2). Two distinct vertices are adjacent if and only if one subspace is contained within the other. We determine various properties of In(Z_{p^s}^n), including its order, vertex degrees, diameter, girth, clique number, and chromatic number. Additionally, we show that In(Z_{p^s}^n) is non-planar. Furthermore, we find the necessary and sufficient conditions for In(Z_{p^s}^n) to be Eulerian.