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

Author

Listed:
  • Isnaini Rosyida

    (Gadjah Mada University
    Semarang State 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)

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.

Suggested Citation

  • Isnaini Rosyida & Jin Peng & Lin Chen & Widodo Widodo & Ch. Rini Indrati & Kiki A. Sugeng, 2018. "An uncertain chromatic number of an uncertain graph based on $$\alpha $$ α -cut coloring," Fuzzy Optimization and Decision Making, Springer, vol. 17(1), pages 103-123, March.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:1:d:10.1007_s10700-016-9260-x
    DOI: 10.1007/s10700-016-9260-x
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    References listed on IDEAS

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    1. Muñoz, Susana & Teresa Ortuño, M. & Ramírez, Javier & Yáñez, Javier, 2005. "Coloring fuzzy graphs," Omega, Elsevier, vol. 33(3), pages 211-221, June.
    2. J. Randall Brown, 1972. "Chromatic Scheduling and the Chromatic Number Problem," Management Science, INFORMS, vol. 19(4-Part-1), pages 456-463, December.
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