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A Graph Theoretic Approach : Petri net

This work attempts to understand some of the basic properties of Petri nets and their relationships to directed bipartite graphs. Different forms of directed graphs are widely used in computer science. Normally various names are given to these structures. E.g. directed acyclic graphs (DAGs), control flow graphs (CFGs), task graphs, generalized task graphs (GTGs), state transition diagrams (STDs), state machines, etc. Some structures might exhibit bisimilarity. The justification for this work is that Petri nets are based on graphs and have some similarities to them. Transforming Petri nets into graphs opens up a whole set of new interesting possible experimentations. Normally this is overlooked. Directed Graphs have a lot of theory and research associated with them. This work could be further developed and used for Petri net evaluation. The related works justifies the reasoning how and why Petri nets are obtained or supported using graphs. The transformation approach can be formal or informal. The main problem tackled is how graphs can be obtained from Petri nets. Possible solutions that use reduction methods to simplify the Petri net are presented. Different methods to extract graphs from the basic or fundamental Petri net classes are explained. Some examples are given and the findings are briefly discussed.