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The Index of a Periodic Graph

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Abstract

For periodic graphs, a special class of infinite, but locally finite graphs, an index theory is developed that can serve in classifying these graphs and that enables connections with various graph invariants as in the case of finite graphs. The index is defined with the aid of certain finite matrices that result rather canonically from reductions of the infinite adjacency operator due to the periodicity. As a central result we derive a sharp global lower bound for the index of any periodic graph.

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Authors and Affiliations

  1. Lehrstuhl für Biomathematik Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Joachim von Below

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  1. Joachim von Below
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von Below, J. The Index of a Periodic Graph. Results. Math. 25, 198–223 (1994). https://doi.org/10.1007/BF03323406

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  • DOI: https://doi.org/10.1007/BF03323406

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