The problem of finding the shortest path including garbage collection is one of the most important problems in environmental research and public health. Usually, the road map has been modeled by a connected undirected graph with the edge representing the path, the weight being the length of the road, and the vertex being the intersection of edges. Hence, the initial problem becomes a problem finding the shortest path on the simulated graph. Although the shortest path problem has been extensively researched and widely applied in miscellaneous disciplines all over the world and for many years, as far as we know, there is no study to apply graph theory to solve the shortest path problem and provide solution to the problem of “assigning vehicles to collect garbage” in Vietnam. Thus, to bridge the gap in the literature of environmental research and public health. We utilize three algorithms including Fleury, Floyd, and Greedy algorithms to analyze to the problem of “assigning vehicles to collect garbage” in District 5, Ho Chi Minh City, Vietnam. We then apply the approach to draw the road guide for the vehicle to run in District 5 of Ho Chi Minh city. To do so, we first draw a small part of the map and then draw the entire road map of District 5 in Ho Chi Minh city. The approach recommended in our paper is reliable and useful for managers in environmental research and public health to use our approach to get the optimal cost and travelling time.