Isnaini Rosyida, Jin Peng, Lin Chen, Widodo Widodo, Ch. Rini Indrati, Kiki A. Sugeng
An uncertain graph is a graph in which the edges are indeterminate and the existence of edges are characterized by belief degrees which are uncertain measures. This paper aims to bring graph coloring and uncertainty theory together. A new approach for uncertain graph coloring based on an α-cut of an uncertain graph is introduced in this paper. Firstly, the concept of α-cut of uncertain graph is given and some of its properties are explored. By means of α-cut coloring, we get an α-cut chromatic number and examine some of its properties as well. Then, a fact that every α-cut chromatic number may be a chromatic number of an uncertain graph is obtained, and the concept of uncertain chromatic set is introduced. In addition, an uncertain chromatic algorithm is constructed. Finally, a real-life decision making problem is given to illustrate the application of the uncertain chromatic set and the effectiveness of the uncertain chromatic algorithm. © 2016, Springer Science+Business Media New York.
Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia; Department of Mathematics, Semarang State University, Semarang, Indonesia; Institute of Uncertain Systems, Huanggang Normal University, Hubei, China; College of Management and Economics, Tianjin University, Tianjin, China; Department of Mathematics, University of Indonesia, Depok, Indonesia
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