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Stability and operations on graphs

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Combinatorial Mathematics III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 452))

Abstract

In this paper we give a detailed survey of stability properties of various combinations of graphs.

We review previous work on unions, joins and (cartesian) products of graphs, and supply further evidence of the unpredictability of the stability index function under cartesian products in that we show that for r>2, the r-cube has stability index 1, which for most values of m and n the product Pm × Pn of two paths has stability index mn-7.

Finally, we discuss the stability properties of compositions (lexicographic products) and coronas of graphs, in particular finding infinite families of such graphs which are stable.

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References

  1. M. Behzad and G. Chartrand, Introduction to the Theory of Graphs (Allyn and Bacon, Boston, 1971).

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  2. D. D. Grant, The stability index of graphs, Combinatorial Mathematics: Proc. Second Australian Conference (D. A. Holton, ed.), Lecture Notes in Mathematics Vol. 403 (1974), to appear, (Springer-Verlag, Berlin-Heidelberg-New York).

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Author information

Author notes

  1. Douglas D. Grant

    Present address: Mathematics Department, University of Reading, Reading, England

Authors and Affiliations

  1. Mathematics Department, University of Melbourne, Victoria

    Douglas D. Grant

Authors
  1. Douglas D. Grant
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Editor information

Anne Penfold Street Walter Denis Wallis

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© 1975 Springer-Verlag

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Grant, D.D. (1975). Stability and operations on graphs. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069551

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  • DOI: https://doi.org/10.1007/BFb0069551

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive

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