Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights

  • Takaaki Fujita
  • Iqbal M. Batiha Al Zaytoonah University of Jordan
  • Muhammad Gulistan
  • Belal Batiha Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid, Jordan
  • Essa Lafi Al Smadi Ajloun National University, Ajloun, Jordan
  • Iqbal Jebril Department of Mathematics, Al-Zaytoonah University of Jordan, Amman, Jordan
DOI: https://doi.org/10.19139/soic-2310-5070-3117
Keywords: Fuzzy Graph, Tree-width, Path-width, Graph Width Parameters

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.
Published
2026-04-04
How to Cite
Fujita, T., Batiha , I. M., Gulistan, M., Batiha, B., Al Smadi, E. L., & Jebril, I. (2026). Tree Decompositions in Fuzzy Graphs: Foundations and Structural Insights. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3117
Issue
Online First
Section
Research Articles
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