Isnaini, Rosyida and Jin, Peng and Lin, Chen and Widodo, - (2016) An uncertain chromatic number of an uncertain graph based on α-cut coloring. Fuzzy Optimization and Decision Making, 17 (1). pp. 103-123. ISSN 1573-2908

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Abstract

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 mea- sures. 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 chro- matic 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 chro- matic 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.

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