Isomorphisms and traversability of directed path graphs

• Autorzy: Hajo Broersma , Xueliang Li
• Języki publikacji: EN

Abstrakty

EN

The concept of a line digraph is generalized to that of a directed path graph. The directed path graph Pₖ(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k+1 vertices or form a directed cycle on k vertices in D. In this introductory paper several properties of P₃(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs D with P₃(D) ≅ D, we show that P₃(D₁) ≅ P₃(D₂) "almost always" implies D₁ ≅ D₂, and we characterize all digraphs with Eulerian or Hamiltonian P₃-graphs.

Słowa kluczowe

EN

directed path graph; line digraph; isomorphism; travers-ability

Kategorie tematyczne

• 05C05: Trees
• 05C45: Eulerian and Hamiltonian graphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2002
• Tom: 22
• Numer: 2
• Strony: 215-228

Daty

wydano

2002

otrzymano

1998-02-23

poprawiono

2002-01-18

Twórcy

autor

Hajo Broersma

• Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

autor

Xueliang Li

• Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China

Bibliografia

• [1] R.E.L. Aldred, M.N. Ellingham, R.L. Hemminger and P. Jipsen, P₃-isomorphisms for graphs, J. Graph Theory 26 (1997) 35-51, doi: 10.1002/(SICI)1097-0118(199709)26:1<35::AID-JGT5>3.0.CO;2-I
• [2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (MacMillan/Elsevier, London/New York, 1976).
• [3] H.J. Broersma and C. Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444, doi: 10.1002/jgt.3190130406.
• [4] F. Harary and R.Z. Norman, Some properties of line digraphs, Rend. Circ. Mat. Palermo 9 (2) (1960) 161-168, doi: 10.1007/BF02854581.
• [5] R.L. Hemminger and L.W. Beineke, Line graphs and line digraphs, in: L.W. Beineke and R.J. Wilson, eds, Selected Topics in Graph Theory (Academic Press, London, New York, San Francisco, 1978).
• [6] X. Li, Isomorphisms of P₃-graphs, J. Graph Theory 21 (1996) 81-85, doi: 10.1002/(SICI)1097-0118(199601)21:1<81::AID-JGT11>3.0.CO;2-V

Identyfikatory

DOI

10.7151/dmgt.1170