Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-23T02:31:40.453Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of line graphs

Published online by Cambridge University Press:  09 April 2009

Douglas D. Grant
Douglas D. Grant
Affiliation:
Department of Mathematics, University of Reading, Reading, England
Rights & Permissions [Opens in a new window]

Abstract

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.

We present in this paper a discussion on some stability properties of line graphs. After relating the semi-stability properties of the line graph of a graph to a concept of Sheehan, we proceed to deduce that, with fully characterised lists of exceptions, the line graphs of trees and unicyclic graphs are semi-stable. We then discuss the problem of deciding which line graphs are stable. Via a discovery of the finite number of graphs G such that both G and its complement have stable line graphs, we show that P4 is the only self-complementary graph whose line graph is stable.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 457 - 466
Copyright
Copyright © Australian Mathematical Society 1976

References

Behzad, M. and Chartrand, G. (1972), Introduction to the Theory of Graphs (Allyn and Bacon, New York, 1972).Google Scholar
Grant, D. D. (1974), ‘The Stability Index of Graphs’, Combinatorial Mathematics: Proceedings of the Second Australian Conference, Lecture Notes in Mathematics No. 403, 29–52 (Springer-Verlag, Berlin, Heidelberg and New York, 1974).CrossRefGoogle Scholar
Harary, F. (1969), Graph Theory (Addison-Wesley, Reading, Mass., 1969).CrossRefGoogle Scholar
Heffernan, P. (1972), Trees (M.Sc. Thesis, University of Canterbury, New Zealand, 1972).Google Scholar
Sheehan, J. (1973), ‘Fixing Subgraphs’, J. Combinatorial Theory, 13, B 226–244.Google Scholar