The objective of this paper is to produce a weighted graph map for path-planning of an autonomous mobile robot(AMR) based on the measurements from a single ultrasonic sensor, which are acquired when the autonomous mobile robot explores unknown indoor circumstance. The AMR navigates in th unknown space by following the wall and gathers the range data using the ultrasonic sensor, from which the occupancy grid map is constructed by associating the range data with occupancy certainties. Then, the occupancy grid map is converted to a weighted graph map suing morphological image processing and thinning algorithms. the path- planning for autonomous navigation of a mobile robot can be carried out based on the occupancy grid map. These procedures are implemented and tested using an AMR, and primary results are presented in this paper.