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The number of trees with nodes of alternate parity

Published online by Cambridge University Press:  24 October 2008

H. I. Scoins
H. I. Scoins
Affiliation:
University Computing LaboratoryNewcastle upon Tyne
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Extract

Interest in the theory of linear graphs has grown recently in several fields which at first sight seem rather far apart. Recent publications include an excellent review by Bryant(1) of electrical network theory, statistical mechanical work by Sykes(2) and in the field of linear programming a paper by Glicksman, Johnson and Eselson (3). It is in this latter field that the subject of this paper arose, but we shall confine attention here to the graph theoretical aspect alone.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 1 , January 1962 , pp. 12 - 16
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Bryant, P. R.The algebra and topology of electrical networks (Proc. Inst. Elect. Engrs., Monograph 414E, 1960).Google Scholar
(2)Sykes, M. F.Some counting theorems in the theory of the Ising model and the excluded volume theory. J. Mathematical Phys. 2 (1961), 52–62.CrossRefGoogle Scholar
(3)Glicksman, S., Johnson, L. and Eselson, L.Coding the transportation problem. Naval Res. Legist. Quart. 7 (1960), 169–83.CrossRefGoogle Scholar
(4)Riordan, J.An introduction to combinatorial analysis. (New York, 1958).Google Scholar
(5)Neville, E. H.The codifying of tree-structures. Proc. Cambridge Philos. Soc. 49 (1953), 381–5.CrossRefGoogle Scholar
(6)Whittaker, E. T. and Watson, G. N.A course of modern analysis, 4th ed. (Cambridge, 1927).Google Scholar
(7)Harary, F. and Prins, G.The number of homeomorphically irreducible trees and other species. Acta Math. 101 (1959), 141–62.CrossRefGoogle Scholar
(8)Riordan, J.The numbers of labelled, coloured and chromatic trees. Acta Math. 97 (1957), 211–25.CrossRefGoogle Scholar