The projection graph P1(R) of a commutative ring R with identity is an undirected graph with the vertex set as the set of all nontrivial elements of R and, x, y are adjacent (x⃩y) iff xy equals x or y. In this paper, projection graphs associated with ring of integers modulo n having prime power characteristic and finite Boolean rings are considered. Stability number and connected domination number are computed. Minimum spanning trees containing connected dominating set and maximum number of pendants are obtained. Planarity is also verified. It is found that the projection graphs of rings of integers modulo n with prime power characteristic possess unique minimum spanning bistars. It is seen that the stability number is maximum iff n is prime. Projection graphs of Boolean rings have multiple minimum spanning strong double brooms. Projection graphs of Boolean rings are proved to be Hamiltonian. Projection graph of Boolean ring of order 16 is found to be Hamiltonian maximal planar graph, in which densely packed hexagons are identified.