Nowadays, graph theory is one of the most popular mathematics and computer science branches. Moreover, because of wide applications, graph theory is used for solving many problems in large modern societies. A subset S of vertices in graph G is called a domination set if each vertex in G is in S or has at least one neighbor in S . This concept has a lot of application and research attraction and many studies have been done on it. Facilities allocation with the least budget by considering the whole regions is one of the important problem in traortation schematization. This thesis applies the concept of domination to locating the facilities stations for the city of Isfahan. For this purpose, the main street intersections in the map of Isfahan city are considered as the vertices and the main streets as edges. Afterward, one algorithm is given to find a domination set with minimum size in the obtained graph. The obtained dominating set could be used for locating the facilities stations such as public parking, police stations and bicycle stations, etc. In particular, since bicycle is a kind of safe and clean public traortation system, the present study results is proposed to use for allocating the bicycle-sharing stations in the Isfahan city.
