An uncertain chromatic number of an uncertain graph based on $$\alpha $$ α -cut coloring

Isnaini Rosyida, Jin Peng (), Lin Chen, Widodo Widodo, Ch. Rini Indrati and Kiki A. Sugeng
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Isnaini Rosyida: Gadjah Mada University
Jin Peng: Huanggang Normal University
Lin Chen: Tianjin University
Widodo Widodo: Gadjah Mada University
Ch. Rini Indrati: Gadjah Mada University
Kiki A. Sugeng: University of Indonesia

Fuzzy Optimization and Decision Making, 2018, vol. 17, issue 1, No 5, 103-123

Abstract: 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 measures. This paper aims to bring graph coloring and uncertainty theory together. A new approach for uncertain graph coloring based on an $$\alpha $$ α -cut of an uncertain graph is introduced in this paper. Firstly, the concept of $$\alpha $$ α -cut of uncertain graph is given and some of its properties are explored. By means of $$\alpha $$ α -cut coloring, we get an $$\alpha $$ α -cut chromatic number and examine some of its properties as well. Then, a fact that every $$\alpha $$ 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.

Keywords: Uncertain graph; $$\alpha $$ α -cut of uncertain graph; $$\alpha $$ α -cut coloring; $$\alpha $$ α -cut chromatic number; Uncertain chromatic set (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10700-016-9260-x

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