The book titled “A Graph Theoretic Approach: Petri Net” is based on Graphs and Petri net concept to optimize any real world problem those are sharing many resources. The text is designed specifically to meet the needs of the students or researchers those are working on optimization problems with little mathematics or computer science background. It gives a new graph theoretic approach to solve and analysis any real life problem. This book is totally applications oriented book which surely benefited and generate new ideas and concepts among researchers in many research areas such as Engineering, Computer Sciences, and Medical Sciences etc. The main objective of this book is to acquaint and familiarize the readers with a new concept and technique, solving real life problems, implementing computational techniques, abstracting mathematical results and proofs etc. Here Petri net relate the same mathematical idea behind any real world problem with a Directed Graph as a pictorial representation of a given relation.