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Characteristic polynomials of spirographs

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Abstract

A class of graphs called spirographs is defined. It is shown that the characteristic polynomials of spirographs can be obtained in terms of the characteristic polynomials of smaller graphs by pruning the spirographs at the spiral points. Elegant recursive relations are derived for many spirographs. Characteristic polynomials of branched spirographs are also obtained.

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Authors and Affiliations

  1. Department of Chemistry, Arizona State University, Tempe, 85287-1604, Arizona, USA

    K. Balasubramanian

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  1. K. Balasubramanian
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Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher-Scholar.

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Balasubramanian, K. Characteristic polynomials of spirographs. J Math Chem 3, 147–159 (1989). https://doi.org/10.1007/BF01166046

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  • DOI: https://doi.org/10.1007/BF01166046

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