A fast minimal storage computational algorithm for determining a minimal spanning tree in a graph

When a system or process is represented as a graph and a unique interconnection between the quantities is desired the problem is one of selecting a spanning tree. Each spanning tree gives a unique path between vertices, but there are many spanning trees for a graph.An algorithm for the selection of a minimal spanning tree for a given weighted connected graph, or a minimal spanning forest for a disconnected weighted graph is presented. The algorithm utilizes sparse matrix techniques, and the basic concept of ring sum operations to obtain the spanning tree, or forest. The minimality of the resultant spanning tree, or forest is proven. In addition, timing and storage requirements are determined. Several cases are studied including the worst case. The only restriction placed on the graphs is that they do not have any isolated vertices.