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- Title
Chromatic Number of Fuzzy Graphs: Operations, Fuzzy Graph Coloring, and Applications.
- Authors
Gong, Zengtai; Zhang, Jing
- Abstract
We focus on fuzzy graphs with crisp vertex sets and fuzzy edge sets. This paper introduces a new concept of chromatic number (crisp) for a fuzzy graph G ˜ (V , E ˜) . Moreover, we define the operations of cap, join, difference, ring sum, direct product, semiproduct, strong product, and Cartesian product of fuzzy graphs. Furthermore, the exact value or the upper boundary of the chromatic number of these fuzzy graphs is obtained based on the α -cuts of G ˜ . Finally, two applications of the chromatic number to solve the timetabling problem and the traffic light problem are analyzed.
- Subjects
FUZZY graphs; GRAPH coloring; FUZZY numbers; FUZZY sets; NUMBER concept; PROBLEM solving
- Publication
Axioms (2075-1680), 2022, Vol 11, Issue 12, p697
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms11120697