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Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations

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Structural Analysis of Complex Networks

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Abstract

We give an overview about some reconstruction problems in graph theory, which are intimately related to integer roots of Krawtchouk polynomials. In this context, Tichy and the author recently showed that a binary Diophantine equation for Krawtchouk polynomials only has finitely many integral solution. Here, this result is extended. By using a method of Krasikov, we decide the general finiteness problem for binary Krawtchouk polynomials within certain ranges of the parameters.

MSC2000: Primary 11D45; Secondary 33C05, 33C45, 39B72

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Acknowledgments

The author is a recipient of an APART-fellowship of the Austrian Academy of Sciences at the University of Waterloo, Canada. He also wishes to express his gratitude to I. Krasikov for several helpful discussions.

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Authors and Affiliations

  1. Faculty of Mathematics, School of Computer Science, University of Waterloo, Waterloo, ON, Canada

    Thomas Stoll

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  1. Thomas Stoll
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Correspondence to Thomas Stoll .

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  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

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Stoll, T. (2011). Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations. In: Dehmer, M. (eds) Structural Analysis of Complex Networks. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4789-6_11

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