On knot separability of hypergraphs and its application towards infectious disease management

Raju Doley; Saifur Rahman; Gayatri Das; Raju Doley; Saifur Rahman; Gayatri Das

doi:10.3934/math.2023505

AIMS Mathematics

2023, Volume 8, Issue 4: 9982-10000. doi: 10.3934/math.2023505

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On knot separability of hypergraphs and its application towards infectious disease management

1.
Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791112, India
2.
Naharkatia H.S. School, Dist. Dibrugarh, Assam, Pin 786610, India

Received: 07 October 2022 Revised: 03 February 2023 Accepted: 16 February 2023 Published: 23 February 2023
MSC : 05C05, 05C38, 05C65, 05C90

The article deals with some theoretical aspects of hypergraph connectivity from the knot view. The strength of knots is defined and investigates some of their properties. We introduce the concept of cut knot and investigate its importance in the connectivity of hypergraphs. We also introduce the concept of hypercycle in terms of knot hyperpath and establish a sufficient condition for a hypergraph to be a hypertree in terms of the strength of knots. Cyclic hypergraph is defined in terms of a permutation on the set of hyperedges and could be an interesting topic for investigation in the sense that it can be linked with the notion of a permutation group. An algorithm is modelled to construct a tree and hypertree from the strength of knots of a hypertree. Lastly, a model of a hypergraph is constructed to control the spread of infection for an infectious disease with the help of the strength of knots.
- strength of knot,
- cut knot,
- knot hypercycle,
- hypertree,
- separable and non-separable hypergraph,
- COVID-19
Citation: Raju Doley, Saifur Rahman, Gayatri Das. On knot separability of hypergraphs and its application towards infectious disease management[J]. AIMS Mathematics, 2023, 8(4): 9982-10000. doi: 10.3934/math.2023505

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Abstract

The article deals with some theoretical aspects of hypergraph connectivity from the knot view. The strength of knots is defined and investigates some of their properties. We introduce the concept of cut knot and investigate its importance in the connectivity of hypergraphs. We also introduce the concept of hypercycle in terms of knot hyperpath and establish a sufficient condition for a hypergraph to be a hypertree in terms of the strength of knots. Cyclic hypergraph is defined in terms of a permutation on the set of hyperedges and could be an interesting topic for investigation in the sense that it can be linked with the notion of a permutation group. An algorithm is modelled to construct a tree and hypertree from the strength of knots of a hypertree. Lastly, a model of a hypergraph is constructed to control the spread of infection for an infectious disease with the help of the strength of knots.

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