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Nonexistence of an extremal graph of a certain type

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

R. G. Stanton ,
S. T. E. Seach  and
D. D. Cowan
R. G. Stanton
Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada
S. T. E. Seach
Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada
D. D. Cowan
Affiliation:
Department of Computer Science, University of WaterlooWaterloo, Ontario, Canada
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Abstract

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Cubic Moore graphs of diameter k on 3.2k−2 vertices do not exist for k > 2. This paper exhibits the first known case of nonexistence for generalized cubic Moore graphs when the number of vertices is just less than the critical number for a Moore graph: the generalized Moore graph on 44 vertices does not exist.

MSC classification

Secondary: 05C35: Extremal problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 55 - 64
Copyright
Copyright © Australian Mathematical Society 1980

References

Cerf, V. G., Cowan, D. D., Mullin, R. C. and Stanton, R. G. (1973), Computer networks and generalized Moore graphs, Proc. Third Manitoba Conference on Numerical Mathematics, Congressus Numerantium IX, Winnipeg (1973), pp. 379–398.Google Scholar
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