Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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HAMILTONIAN PROPERTIES OF ENHANCED HONEYCOMB NETWORKS

  • M. SOMASUNDARI (Department of Mathematics, Hindustan Institute of Technology and Science) ;
  • A. RAJKUMAR (Department of Mathematics, Hindustan Institute of Technology and Science) ;
  • F. SIMON RAJ (Department of Mathematics for Excellence, Saveetha School of Engineering, Saveetha institute of Medical and Technical Sciences) ;
  • A. GEORGE (Department of Mathematics, Periyar Maniammai University)
  • Received : 2023.08.19
  • Accepted : 2024.03.07
  • Published : 2024.07.30
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Abstract

A cycle in a graph G that contains all of its vertices is said to be the Hamiltonian cycle of that graph. A Hamiltonian graph is one that has a Hamiltonian cycle. This article discusses how to create a new network from an existing one, such as the Enhanced Honeycomb Network EHC(n), which is created by adding six new edges to each layer of the Honeycomb Network HC(n). Enhanced honeycomb networks have 9n2 + 3n - 6 edges and 6n2 vertices. For every perfect sub-Honeycombe topology, this new network features six edge disjoint Hamiltonian cycles, which is an advantage over Honeycomb. Its diameter is (2n + 1), which is nearly 50% lesser than that of the Honeycomb network. Using 3-bit grey code, we demonstrated that the Enhanced Honeycomb Network EHC(n) is Hamiltonian.

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Acknowledgement

I would like to thank the reviewers.

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