The λ-Fold Spectrum Problem for the Orientations of the Eight-Cycle

Creative Commons License

DURUKAN ODABAŞI Ş., Odabaşı U.

Symmetry, cilt.15, sa.10, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 10
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/sym15101930
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: complete symmetric digraph, decompositions, orientations of an eight-cycle, λ-fold spectrum problem
  • İstanbul Üniversitesi Adresli: Evet

Özet

A D-decomposition of a graph (or digraph) G is a partition of the edge set (or arc set) of G into subsets, where each subset induces a copy of the fixed graph D. Graph decomposition finds motivation in numerous practical applications, particularly in the realm of symmetric graphs, where these decompositions illuminate intricate symmetrical patterns within the graph, aiding in various fields such as network design, and combinatorial mathematics, among various others. Of particular interest is the case where G is (Formula presented.), the (Formula presented.) -fold complete symmetric digraph on v vertices, that is, the digraph with (Formula presented.) directed edges in each direction between each pair of vertices. For a given digraph D, the set of all values v for which (Formula presented.) has a D-decomposition is called the (Formula presented.) -fold spectrum of D. An eight-cycle has 22 non-isomorphic orientations. The (Formula presented.) -fold spectrum problem has been solved for one of these oriented cycles. In this paper, we provide a complete solution to the (Formula presented.) -fold spectrum problem for each of the remaining 21 orientations.