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On one of Graffiti's conjecture (583)

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Abstract

In the paper, a counterexample of the Graffiti's conjecture (583) is given out which proves the conjecture is false. And the best bounds of I(T)+a′(T) are got, where T denotes a tree, I(T) denotes the inverse degree of T and a′(T) is the matching of T.

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References

  1. F. R. K. Chung. The average distance and the independence number,J. of Graph Theory,12 (1988), 229–235.

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  2. I. A. Bondy and U. S. R. Murty,Graph Theory with Applications, The MacMillan Press Ltd. (1976).

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Authors and Affiliations

  1. Heilongjiang Hydraulic Engineering College, 150086, Harbin, P. R. China

    Wang Liuxing

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  1. Wang Liuxing
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Additional information

Communicated by Liu Renhuai

Project supported by the NSF of Gansu Province and Railway Ministry

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Liuxing, W. On one of Graffiti's conjecture (583). Appl Math Mech 18, 381–383 (1997). https://doi.org/10.1007/BF02457552

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  • DOI: https://doi.org/10.1007/BF02457552

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