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The semi-stability of lexicographic products

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Part of the Lecture Notes in Mathematics book series (LNM,volume 622)

Abstract

We prove Grant's conjecture that, for all graphs G and H with H ≇ K1, the lexicographic product G[H] is semi-stable at (v, w) if H is semi-stable at w. Thus we can conclude that G[H] is semi-stable at (v, w) if and only if H is semi-stable at w.

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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, "Stability and operations on graphs", Lecture Notes in Mathematics No. 452, Springer-Verlag, Berlin, 1975, 116–135.

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  3. D.A. Holton, "Two applications of semi-stable graphs", Discrete Maths., 4, 1973, 151–158.

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  4. D.A. Holton and D.D. Grant, "Regular graphs and stability", J. Austral. Math. Soc., 20, Series A, 1975, 377–384.

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© 1977 Springer-Verlag

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Holton, D.A., Stacey, K.C., McAvaney, K.L. (1977). The semi-stability of lexicographic products. In: Little, C.H.C. (eds) Combinatorial Mathematics V. Lecture Notes in Mathematics, vol 622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069186

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  • DOI: https://doi.org/10.1007/BFb0069186

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08524-9

  • Online ISBN: 978-3-540-37020-8

  • eBook Packages: Springer Book Archive