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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
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Abstract

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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

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