Abstract
Oriented 2-factorable graphs are reduced to bouquets by permutation voltage assignment in this paper. Introducing the concept ofk-class index of a permutation group, various oriented 2-factorable graphs are enumerated in this paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. L. Biggs and A. T. White,Permutation Groups and Combinatoric Structure, Cambridge University Press (1979).
F. Harary and E. M. Palmer,Graphic Enumeration, Academic Press, New York (1973).
J. L. Gross and T. W. Tucker,Topological Graph Theory, John Wiley & Sons, 1987.
D. M. Jackson and T. I. Visentin,A character theoretic approach to embeddings of rooted maps in an orientable surface of given genus, Trans. Amer. Math. Soc.322 (1990), 343–363.
V. Krishnamurthy,Combinatorics: Theory and Application, Ellis Horwood Limited, 1986.
Linfan Mao,On the panfactorial property of Cayley graphs, J. Math. Res. & Exp.,22(3) (2002), 383–390.
Linfan Mao and Yanpei Liu,On the Roots on Orientable Embeddings of Graph, Acta Math. Scientia,23A(3), 287–293.
Linfan Mao and Yanpei Liu,Group action for enumerating maps on surfaces, J. Appl. Math. & Computing13(1–2) (2003), 201–215.
G. Polya and R. C. Read,Combinatorial Enumeration of Graphs, Groups and Chemical Components, Springer, 1987.
R. C. Read and R. W. Robinson,Enumeration of labelled multigraphs by degree parities, Discrete Math.42 (1982), 99–105.
W. T. Tutte,Graph Theory, Cambridge University Press, 2001.
A. T. White,Graphs of Group on Surfaces-interactions and models, Elsevier Science B. V. (2001).
Xu Mingyao et al,Introduction to finite groups (II), Science Press, Beijing (1999).
Yanpei Liu,Enumerative Theory of Maps, Kluwer Academic Publisher, Dordrecht/Boston/London (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Linfan Mao is a postdoctor in Academy of Mathematics and System Sciences of Chinece Academy of Science. His research interests focus on topological graph theory, particularly in the enumeration of embeddings and maps and hamiltonian graphs.
Feng Tian is a professor in Academy of Mathematics and System Sciences of Chinese Academy of Science. His research interests focus on graph structure, particularly in the hamiltonian graph theory.
Rights and permissions
About this article
Cite this article
Mao, L., Tian, F. On oriented 2-factorable graphs. JAMC 17, 25–38 (2005). https://doi.org/10.1007/BF02936038
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02936038