Decompositions of complete symmetric directed graphs into the oriented heptagons

ODABAŞI U.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.4, pp.1660-1667, 2021 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2007-54
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1660-1667
  • Keywords: Decomposition, directed graph, orientations of a heptagon, CYCLE DECOMPOSITIONS, OBERWOLFACH PROBLEM
  • Istanbul University-Cerrahpasa Affiliated: Yes

Abstract

The complete symmetric directed graph of order v, denoted by K-v*, is the directed graph on v vertices that contains both arcs (x, y) and (y, x) for each pair of distinct vertices x and y. For a given directed graph D, the set of all v for which K-v* admits a D-decomposition is called the spectrum of D-decomposition. There are 10 nonisomorphic orientations of a 7-cycle (heptagon). In this paper, we completely settled the spectrum problem for each of the oriented heptagons.