Proposing a Pure Binary Linear Programming (PBLP) Model to Discover Eulerian Circuits in Complete Graphs

Known as a branch of Discrete Mathematics (DM), the Graph Theory (GT) describes and solves problems of discrete nature through nodes (i.e., vertices) and arcs (i.e., edges). In this regard, a prominent problem is to find the Eulerian circuits. This paper indicates that the problem can be analyzed through operations research methods. In more general terms, finding the Eulerian circuits could be considered a pathfinding problem. Hence, this paper proposes a pure binary mathematical model to describe the relationship between the variables employed to find the Eulerian circuits. All the analyses in this paper were performed in MATLAB. The proposed model can be solved by many optimization software applications. Finally, several numerical examples are presented and solved through the proposed method. All the analyses in this paper were performed in MATLAB. This paper indicated that the problem(Eulerian Circuits in Complete Graphs) could be studied and solved from the perspective of operations research.