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An extension of a theorem of König on graphs

Published online by Cambridge University Press:  26 February 2010

J. W. Archbold  and
C. A. B. Smith
J. W. Archbold
Affiliation:
University College, London
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Extract

Let G be a graph with b+v vertices, each of the b vertices P1, …, Pb having valency k and each of the remaining v vertices Q1 …, Qv having valency r, and each edge joining a vertex Pm to a vertex Qn. Suppose also that b≥v; then r≥k since bk = vr.

Type
Research Article
Information
Mathematika , Volume 9 , Issue 1 , June 1962 , pp. 9 - 10
Copyright
Copyright © University College London 1962

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References

1.König, D., Theorie der endlichen und unendlichen Graphen (New York, 1950), 170–178.Google Scholar
2.Archbold, J. W., “Incidence matrices”, Mathematika, 7 (1960), 41–49.CrossRefGoogle Scholar
3.Hall, M. Jr., “Cyclic projective planes”, Duke Math. J., 14 (1947), 1079–1090.Google Scholar