Covering problem on fuzzy graphs and its application in disaster management system

Nowadays the fuzzy graphs gained popularity due to their wide applications in different areas of science, engineering, social sciences, etc.In this paper, we consider covering problem in fuzzy graph. Different types of covering problems have been defined in this paper. Almost all problems are new. For each of these problems separate study is required. Also, the covering set, strong covering set, minimal covering set, etc., are defined and explained with examples. In a graph, each vertex can cover only those vertices that lie within its covering radius along shortest path and no vertex can cover itself. Here, an algorithm is designed to find the different types of covering sets on a fuzzy graph. An imprecise number, instead of a real number, namely interval number and triangular fuzzy number are considered as arc length of a fuzzy graph. To the best of our knowledge no works are available for covering problem on fuzzy graphs/networks. An application of covering set in natural disaster management is discussed to highlight the importance of the covering problem. In this application, an algorithm is designed to find all the facility vertices (or supply vertices) for given vertex and covering radius.