Abstract
A special graph, the PS graph, is introduced and an algorithm is developed to generate all trees of such graphs. It is proved that for any given graph, G there exists certain number of PS graphs, obtained from G, such that the collection of all trees of all such PS graph span all trees of G with no duplication. In addition to a number of properties of PS graphs indicated, the procedure seems very useful for topological analysis and design of networks, or any other types of systems that can be represented by a linear graph.
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