Decomposition Hamilton in Cayley Graphs with Certain Invers Generator of Dihedral-
              
                2
                n
              
            $$2n$$ Group

Astri Kumala; Hery Susanto; Desi Rahmadani; Wahyu Henky Irawan

doi:10.2991/978-94-6463-148-7_42

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Decomposition Hamilton in Cayley Graphs with Certain Invers Generator of Dihedral- 2 n $$2n$$ Group

Authors

Astri Kumala¹, Hery Susanto¹^{, *}, Desi Rahmadani¹, Wahyu Henky Irawan²

¹State University of Malang, Jl. Semarang 5, Malang, Indonesia

²Universitas Islam Negeri Maulana Malik Ibrahim Malang, Jl. Gajayana 50, Malang, Indonesia

^*Corresponding author. Email: hery.susanto.fmipa@um.ac.id

Corresponding Author

Hery Susanto

Available Online 29 May 2023.

DOI: 10.2991/978-94-6463-148-7_42 How to use a DOI?
Keywords: Cayley graph; decomposition; dihedral group; Hamilton cycle; 1-factor
Abstract: The Hamilton decomposition of graph G is a partition of the edge set into a Hamilton cycle and 1-factor if the vertex degree is odd or a partition into a Hamilton cycle if the degree of the vertex is even. In 2020, the focus was on determining the Hamilton decomposition of a Cayley graph in the dihedral- 2 p group, where p is a single prime. In this paper, the Hamiltonian decomposition of the Cayley graph will be determined from the dihedral- 2 n group, with n ≥ 3 . This research aims to determine Hamiltonian decomposition, which focuses on generating { r n - 1 , s } from dihedral groups. The research method is to determine the dihedral- 2 n group, determine the set of vertices and the set of edges of the Cayley graph, construct the Cayley graph generated by { r n - 1 , s } , and decompose the Cayley graph using Hamiltonian. The vertex degree of the Cayley graph, constructed by the dihedral- 2 n group and generated by { r n - 1 , s } , , is an odd vertex. Graph decomposition results are a Hamilton cycle and 1-factor (perfect matching).
Copyright: © 2023 The Author(s)
Open Access: Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title: Proceedings of the 12th International Conference on Green Technology (ICGT 2022)
Series: Advances in Engineering Research
Publication Date: 29 May 2023
ISBN: 10.2991/978-94-6463-148-7_42
ISSN: 2352-5401
DOI: 10.2991/978-94-6463-148-7_42 How to use a DOI?
Open Access: Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

ris enw bib

TY  - CONF
AU  - Astri Kumala
AU  - Hery Susanto
AU  - Desi Rahmadani
AU  - Wahyu Henky Irawan
PY  - 2023
DA  - 2023/05/29
TI  - Decomposition Hamilton in Cayley Graphs with Certain Invers Generator of Dihedral-
              
                2
                n
              
            $$2n$$ Group
BT  - Proceedings of the 12th International Conference on Green Technology (ICGT 2022)
PB  - Atlantis Press
SP  - 423
EP  - 431
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-148-7_42
DO  - 10.2991/978-94-6463-148-7_42
ID  - Kumala2023
ER  -

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