# Destroying symmetry by orienting edges: complete graphs and complete bigraphs

Frank Harary; Michael S. Jacobson

Discussiones Mathematicae Graph Theory (2001)

- Volume: 21, Issue: 2, page 149-158
- ISSN: 2083-5892

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topFrank Harary, and Michael S. Jacobson. "Destroying symmetry by orienting edges: complete graphs and complete bigraphs." Discussiones Mathematicae Graph Theory 21.2 (2001): 149-158. <http://eudml.org/doc/270313>.

@article{FrankHarary2001,

abstract = {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.},

author = {Frank Harary, Michael S. Jacobson},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {oriented graph; automorphism group; identity orientation number; identity oriented forest},

language = {eng},

number = {2},

pages = {149-158},

title = {Destroying symmetry by orienting edges: complete graphs and complete bigraphs},

url = {http://eudml.org/doc/270313},

volume = {21},

year = {2001},

}

TY - JOUR

AU - Frank Harary

AU - Michael S. Jacobson

TI - Destroying symmetry by orienting edges: complete graphs and complete bigraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2001

VL - 21

IS - 2

SP - 149

EP - 158

AB - 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.

LA - eng

KW - oriented graph; automorphism group; identity orientation number; identity oriented forest

UR - http://eudml.org/doc/270313

ER -

## References

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- [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. Zbl0084.19304
- [8] F. Harary and R.W. Robinson, The number of identity oriented trees (to appear). Zbl0311.05102
- [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. Zbl0307.05115
- [10] L.V. Quintas, Extrema concerning asymmetric graphs, J. Combin. Theory 5 (1968) 115-125. Zbl0157.55004

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