Hostname: page-component-cb9f654ff-mwwwr Total loading time: 0 Render date: 2025-09-02T11:16:38.411Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimally strong digraphs

Published online by Cambridge University Press:  20 January 2009

Dennis P. Geller
Dennis P. Geller
Affiliation:
Logic of Computers Group, University of Michigan, Ann Arbor, Michigan
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.

Dirac (2) and Plummer (5) independently investigated the structure of minimally 2-connected graphs G, which are characterized by the property that for any line x of G, G–x is not 2-connected. In this paper we investigate an analogous class of strongly connected digraphs D such that for any arc x, D–x is not strong. Not surprisingly, these digraphs have much in common with the minimally 2-connected graphs, and a number of theorems similar to those in (2) and (5) are proved, notably our Theorems 9 and 12.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 15 - 22
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Berge, C., The Theory of Graphs and its Applications (Wiley, New York, 1962).Google Scholar
(2) Dirac, G. A., Minimally 2-connected graphs, J. reine angew. Math. 228 (1968), 204–216.Google Scholar
(3) Harary, F., Graph Theory (Addison-Wesley, Reading, 1969).Google Scholar
(4) Harary, F., Norman, R. Z., and Cartwright, D., Structural Models: an Introduction to the Theory of Directed Graphs (Wiley, New York, 1965).Google Scholar
(5) Plummer, M. D., On blocks with a minimal number of lines, Trans. Amer. Math. Soc., to appear.Google Scholar
(6) Robbins, H. E., A theorem on graphs, with an application to traffic control, Amer. Math. Monthly, 46 (1939), 281–283.CrossRefGoogle Scholar