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The Moore Bound for Irregular Graphs

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Abstract.

 What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10).

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Authors and Affiliations

  1. Mathematics and Computer Science, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel. e-mail: noga@math.tau.ac.il, , , , , , IL

    Noga Alon

  2. Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel e-mail: shlomoh@cs.huji.ac.il, , , , , , IL

    Shlomo Hoory

  3. Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel e-mail: nati@cs.huji.ac.il, , , , , , IL

    Nathan Linial

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  1. Noga Alon
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  2. Shlomo Hoory
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  3. Nathan Linial
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Received: June 27, 2000 Final version received: July 3, 2001

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Alon, N., Hoory, S. & Linial, N. The Moore Bound for Irregular Graphs. Graphs Comb 18, 53–57 (2002). https://doi.org/10.1007/s003730200002

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  • DOI: https://doi.org/10.1007/s003730200002

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