Destroying symmetry by orienting edges: complete graphs and complete bigraphs

• Autorzy: Frank Harary , Michael S. Jacobson
• Języki publikacji: EN

Abstrakty

EN

Our purpose is to introduce the concept of determining the smallest number of edges of a graph which can be oriented so that the resulting mixed graph has the trivial automorphism group. We find that this number for complete graphs is related to the number of identity oriented trees. For complete bipartite graphs $K_{s,t}$, s ≤ t, this number does not always exist. We determine for s ≤ 4 the values of t for which this number does exist.

Słowa kluczowe

EN

oriented graph; automorphism group

Kategorie tematyczne

• 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 149-158

Daty

wydano

2001

otrzymano

1999-12-21

poprawiono

2001-07-02

Twórcy

autor

Frank Harary

• Department of Computer Science, New Mexico State University, Las Cruces, NM 88003, USA

autor

Michael S. Jacobson

• Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

Bibliografia

• [1] G. Chartrand and L. Lesniak, Graphs & Digraphs, third edition (Chapman & Hall, New York, 1996).
• [2] F. Harary, Graph Theory (Addison-Wesley, Reading MA 1969).
• [3] F. Harary, R. Norman and D. Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs (Wiley, New York, 1965).
• [4] F. Harary and E.M. Palmer, Graphical Enumeration (Academic Press, New York, 1973).
• [5] A. Blass and F. Harary, Properties of almost all graphs and complexes, J. Graph Theory 3 (1979) 225-240, doi: 10.1002/jgt.3190030305.
• [6] E.M. Palmer, Graphical Evolution (Wiley, New York, 1983).
• [7] F. Harary and G. Prins, The number of homeomorphically irreducible trees and other species, Acta Math. 101 (1959) 141-162, doi: 10.1007/BF02559543.
• [8] F. Harary and R.W. Robinson, The number of identity oriented trees (to appear).
• [9] D.J. McCarthy and L.V. Quintas, A stability theorem for minimum edge graphs with given abstract automorphism group, Trans. Amer. Math. Soc. 208 (1977) 27-39, doi: 10.1090/S0002-9947-1975-0369148-4.
• [10] L.V. Quintas, Extrema concerning asymmetric graphs, J. Combin. Theory 5 (1968) 115-125.

Identyfikatory

DOI

10.7151/dmgt.1139