GRAF CAYLEY PADA S_n

Okal, Marye; Kiftiah, Mariatul; Fran, Fransiskus

doi:10.26418/bbimst.v8i1.30506

Cited by 1 publication

(3 citation statements)

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“…Here are various studies on algebraic graphs, such as the primitive edge of the Cayley graph on the abelian group and the dihedral group, which describes an edge-primitive graph if the automorphism group operates primitively on the edge set [5]. Cayley graph illustrating the symmetry group and the number of isomorphic graph patterns produced [6]. The whole categorization of graph products from groups to abelian that compose Cayley graphs as described by the standard is planar [7].…”

Section: Introductionmentioning

confidence: 99%

“…(continued) , sr , sr3 , sr 2 sr 4 , sr 3 , sr5 , sr4 , sr5 , r 2 , r 3 , r 2 , r 4 , r 3 , r 5 , r 4 , , r , r 3 , sr 4 , r4 , sr 3 , r 5 , sr 2 , r 6 , sr , , sr , sr 3 , sr 2 sr 4 , sr 3 , sr5 , sr 4 , (sr 6 , sr 5 ) sr6 , r 2 , r 3 , r 2 , r 4 , r 3 , r 5 , r 4 , r 6 , r 5 , r 7 , r 6 , , r , r 3 , sr 5 , r 4 , sr 4 , r 5 , sr 3 , r 6 , sr 2 , r 7 , sr , sr 7 , sr6 …”

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“…(continued) , sr , sr 3 , sr 2 sr 4 , sr 3 , sr5 , sr 4 , (sr 6 , sr 5 ) sr7 , sr6 , sr 8 , sr7 , sr 8 , r 2 , r 3 , r 2 , r 4 , r 3 , r 5 , r 4 , r 6 , r 5 , r 7 , r 6 , r 8 , r 7 , r 9 , r 8 , 1, r9 …”

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

Kumala,

Susanto,

Rahmadani

et al. 2023

Advances in Engineering Research

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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-2p group, where p is a single prime. In this paper, the Hamiltonian decomposition of the Cayley graph will be determined from the dihedral-2n 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-2n 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-2n group and generated by {r n−1 , s}, , is an odd vertex. Graph decomposition results are a Hamilton cycle and 1-factor (perfect matching).

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Section: Introductionmentioning

confidence: 99%