Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Article
Publication Date
2024
Abstract
Hypergraphs extend traditional graphs by allowing edges (known as hyperedges) to connect more than two vertices, rather than just pairs. This paper explores fundamental problems and algorithms in the context of SuperHypergraphs, an advanced extension of hypergraphs enabling modeling of hierarchical and complex relationships. Topics covered include constructing SuperHyperGraphs, recognizing SuperHyperTrees, and computing SuperHyperTree-width. We address a range of optimization problems, such as the SuperHy-pergraph Partition Problem, Reachability, Minimum Spanning SuperHypertree, and Single-Source Shortest Path. Furthermore, adaptations of classical problems like the Traveling Salesman Problem, Chinese Postman Problem, and Longest Simple Path Problem are presented in the SuperHypergraph framework.
Publication Title
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
Volume
2
First Page
240
Last Page
272
Keywords
Superhypergraph, Hypergraph, Tree-width, Algorithm.
Recommended Citation
Fujita, Takaaki and Florentin Smarandache.
"Fundamental Computational Problems and Algorithms for SuperHyperGraphs."
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
