Products Of Digraphs And Their Competition Graphs

• Autorzy: Martin Sonntag , Hanns-Martin Teichert
• Języki publikacji: EN

Abstrakty

EN

If D = (V, A) is a digraph, its competition graph (with loops) CGl(D) has the vertex set V and {u, v} ⊆ V is an edge of CGl(D) if and only if there is a vertex w ∈ V such that (u, w), (v, w) ∈ A. In CGl(D), loops {v} are allowed only if v is the only predecessor of a certain vertex w ∈ V. For several products D1 ⚬ D2 of digraphs D1 and D2, we investigate the relations between the competition graphs of the factors D1, D2 and the competition graph of their product D1 ⚬ D2.

Słowa kluczowe

EN

competition graph; product of digraphs

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments
• 05C76: Graph operations (line graphs, products, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 1
• Strony: 43-58

Daty

wydano

2016-02-01

otrzymano

2014-11-20

poprawiono

2015-04-07

zaakceptowano

2015-04-07

online

2016-01-19

Twórcy

autor

Martin Sonntag

• Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Prüferstraße 1, D-09596 Freiberg, Germany

autor

Hanns-Martin Teichert

• Institute of Mathematics, University of Lübeck, Ratzeburger Allee 160, D-23562 Lübeck, Germany

Bibliografia

• [1] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer, London, 2001).
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• [3] W. Imrich and S. Klavžar, Product Graphs (John Wiley & Sons, Inc., New York, 2000).
• [4] S.R. Kim, The competition number and its variants, in: Quo vadis, graph theory?, J. Gimbel, J.W. Kennedy and L.V. Quintas (Eds.), Ann. Discrete Math. 55 (1993) 313–326. doi:10.1016/s0167-5060(08)70396-0[Crossref]
• [5] J.R. Lundgren, Food webs, competition graphs, competition-common enemy graphs and niche graphs, in: Applications of combinatorics and graph theory to the biological and social sciences, F. Roberts (Ed.), (IMA 17, Springer, New York, 1989) 221–243. doi:10.1007/978-1-4684-6381-1_9[Crossref]
• [6] F.S. Roberts, Competition graphs and phylogeny graphs, in: Graph theory and combinatorial biology, L. Lovász (Ed.), (Proc. Int. Colloqu. Balatonlelle (Hungary) 1996, Bolyai Soc. Math. Studies 7, Budapest, 1999) 333–362.
• [7] M. Sonntag and H.-M. Teichert, Competition hypergraphs, Discrete Appl. Math. 143 (2004) 324–329. doi:10.1016/j.dam.2004.02.010[Crossref]
• [8] M. Sonntag and H.-M. Teichert, Competition hypergraphs of products of digraphs, Graphs Combin. 25 (2009) 611–624. doi:10.1007/s00373-005-0868-9[Crossref]

Identyfikatory

DOI

10.7151/dmgt.1851