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Algorithms for generalized stability numbers of tree graphs

Published online by Cambridge University Press:  09 April 2009

D. E. Daykin  and
C. P. Ng
D. E. Daykin
Affiliation:
Department of Mathematics University of Malaya Kuala Lumpur, Malaysia
C. P. Ng
Affiliation:
Department of Mathematics University of Malaya Kuala Lumpur, Malaysia
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In this paper we give some algorithms for determining αw(T) and βw(T), the generalized internal and external stability numbers respectively, of a finite directed tree graph T whose nodes are weighted by a function w. We define αw(T) and βw in section 2. When w gives every node of T the weight 1 then αw(T) = α(T) and βw(T) = β(T) where α(T) and β(T) are the usual stability numbers.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1966 , pp. 89 - 100
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Berge, C., The Theory of Graphs (London, 1962).Google Scholar
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[4]Scoins, H. I., “The number of trees with nodes of alternate parity”, Proc. Cambridge Philos. Soc. 58 (1962), 12–16.CrossRefGoogle Scholar