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Knots and Knot-Hyperpaths in Hypergraphs

Author

Listed:
  • Saifur Rahman

    (Department of Mathematics, Rajiv Gandhi University, Rono Hills, Itanagar 791112, India)

  • Maitrayee Chowdhury

    (Department of Mathematics, Rajiv Gandhi University, Rono Hills, Itanagar 791112, India)

  • Firos A.

    (Department of Computer Science and Engineering, Rajiv Gandhi University, Rono Hills, Itanagar 791112, India)

  • Irina Cristea

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

Abstract

This paper deals with some theoretical aspects of hypergraphs related to hyperpaths and hypertrees. In ordinary graph theory, the intersecting or adjacent edges contain exactly one vertex; however, in the case of hypergraph theory, the adjacent or intersecting hyperedges may contain more than one vertex. This fact leads to the intuitive notion of knots, i.e., a collection of explicit vertices. The key idea of this manuscript lies in the introduction of the concept of the knot, which is a subset of the intersection of some intersecting hyperedges. We define knot-hyperpaths and equivalent knot-hyperpaths and study their relationships with the algebraic space continuity and the pseudo-open character of maps. Moreover, we establish a sufficient condition under which a hypergraph is a hypertree, without using the concept of the host graph.

Suggested Citation

  • Saifur Rahman & Maitrayee Chowdhury & Firos A. & Irina Cristea, 2022. "Knots and Knot-Hyperpaths in Hypergraphs," Mathematics, MDPI, vol. 10(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:424-:d:737194
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