Year: 2025
Type: article
Abstract: Let G be an n-regular graph. A sequentially perfect one-factorization is a decomposition of G into one-factors, such that union of any two consecutive one-factors gives a hamiltonian cycle, and also if the union of two consecutive one-factors forms a two regular graph, then this property is termed as sequentially uniform. For any two graphs G and H their product [Cartesian, Tensor, Wreath] has the vertex set {(g, h); g belongs to V(G) and h belongs to V(H)}. The Cartesian Product G Cartesian Product H has the edge set such that two vertices (g1, h1) and (g2, h2) are adjacent if they differ in exactly one coordinate, and the corresponding vertices in that graph are adjacent; in the tensor product G Tensor Product H two vertices (g1, h1) and (g2, h2) are adjacent only if both g1 is adjacent to g2 in G and h1 is adjacent to h2 in H; in the wreath product G Wreath Product H the edge set is E(G Wreath Product H) = {(g1, h1) (g2, h2) : g1g2 belongs to E(G) or g1=g2 and h1h2 belongs to E(H)}. In this paper it is proved that for all even m > 2 and odd n ≥ 3, there exists sequentially perfect and sequentially uniform one-factorizations in Cm Cartesian Product Cn, Cm Tensor Product Cn and Cm Wreath Product Cn.
Authors: Jamuna Loganathan, Hemalatha Palanisamy
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414670152