Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-09T09:19:33.918Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
[2]Maghout, K., “Sur la détermination des nombres de stabilité et du nombre chromatique d'un graphe”, C. R. Acad. Sci. Paris 248 (1959), 3522–3.Google Scholar
[3]Ore, O., Theory of Graphs (Amer. Math. Soc. Coll. Pub. Vol XXXVIII, 1962).Google Scholar
[4]Scoins, H. I., “The number of trees with nodes of alternate parity”, Proc. Cambridge Philos. Soc. 58 (1962), 12–16.CrossRefGoogle Scholar