Authors propose parallel/pipelined and parallel/iterative spanning tree generators for directed and undirected graphs based on graph theory algorithms using adjacency matrices. A generator employing iterative logic circuits with high regularity suitable for VLSI implementation can be realized with O(n**2) gates where n is the number of nodes in a given graph. This generator can compute a spanning tree of an nXn adjacency matrix within O(n**2) gate delays. The organizations of spanning tree generators are discussed.