Knots and Knot-Hyperpaths in Hypergraphs

Saifur Rahman, Maitrayee Chowdhury, Firos A. and Irina Cristea
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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

Mathematics, 2022, vol. 10, issue 3, 1-13

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.

Keywords: hypergraph; hyperpath; hypertree; knot; hypercontinuity; equivalent hyperpaths (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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