A graph theory‐based methodology is proposed for the sewer system optimization problem in this study. Sewer system optimization includes two subproblems: layout optimization and hydraulic design optimization, which can be solved independently or solved simultaneously. No matter which method is chosen for the solution of the optimization problem, a feasible layout that satisfies the restrictions of the sewer system must be obtained in any step of the solution. There are two different layout options encountered: the layouts containing all sewer links and the layouts not containing all sewer links. The method proposed in this study generates a feasible sewer layout that contains all sewer links and satisfies all restrictions of a sanitary sewer system by using graph theory without any additional strategies unlike other studies. The method is applied to two different case studies. The results of the case studies have shown that graph theory is well applicable to sewer system optimization and the methodology proposed based on it is capable of generating a feasible layout. This study is expected to stimulate the use of graph theory on similar studies.

For a vertex of a graph , the lower connectivity, denoted by , is the smallest number of vertices that contains and those vertices whose deletion from produces a disconnected or a trivial graph. The average lower connectivity denoted by is the value . It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs.