In this paper, an exploration path algorithm is proposed for mobile robots to make a map of a working environment. The exploration task is defined as a problem of generating minimal-cost path, in which robots go through several observation points and observe a working environment. Both number of the observation points and path length should be minimized. The proposed algorithm has two characteristics: efficiency in exploration and adaptability to dynamic environmental changes. Our method can be realized with the combination of (a) distribution of observation points by a reaction-diffusion equation on a graph, and (b) generation of a Hamiltonian circle that connects all observation points. The observation points dynamically change their arrangements in accordance with the recognized environmental situation. The calculation cost for exploration path generation is shown to be in order of N1.5, where N is the number of the observation points. Our method can be extended into cooperative exploration path planning method. Our method homogenized the arrangement of the observation points, then only a basic partition method can equally part exploration task for each robot. The effectiveness of our method is shown by both simulation and real robot experiments.