Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights
Abstract
A Fuzzy Graph extends classical graph theory by incorporating uncertainty, assigning a membership degree to each edge. Tree-width is a basic metric that assesses how much a graph resembles a tree [31, 32], making it an essential tool in algorithm design and combinatorial optimization. Path-width quantifies how much a graph resembles a path, using smallest bag size minus one in path-decomposition of the graph. The main aim of this work is to present the Fuzzy Tree-Decomposition and Fuzzy Path-Decomposition, extending the classical notions of tree- and path-decompositions to the realm of fuzzy graphs. We anticipate that these novel ideas will expand the possible uses of fuzzy graphs and encourage more investigation into the mathematical structure of graph-width parameters.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Multi-Criteria Decision Making
Advanced Graph Theory Research
Publication details
- Journal / source
- Statistics Optimization & Information Computing
- Publisher
- International Academic Press
- Volume
- 16
- Issue
- 1
- Pages
- 312–326
- Publication date
- 4 April 2026