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International Workshop on Frontiers in Algorithmics

FAW 2015: Frontiers in Algorithmics pp 45–51Cite as

Efficient Computation of the Characteristic Polynomial of a Threshold Graph

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9130))

Abstract

An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph. Threshold graphs were introduced by Chvátal and Hammer, as well as by Henderson and Zalcstein in 1977. A threshold graph is obtained from a one vertex graph by repeatedly adding either an isolated vertex or a dominating vertex, which is a vertex adjacent to all the other vertices. Threshold graphs are special kinds of cographs, which themselves are special kinds of graphs of clique-width 2. We obtain a running time of \(O(n \log ^2 n)\) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time.

M. Fürer—Research supported in part by NSF Grant CCF-1320814.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Pennsylvania State University, University Park, State College, PA, 16802, USA

    Martin Fürer

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  1. Martin Fürer
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Correspondence to Martin Fürer .

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Editors and Affiliations

  1. Central South University, Changsha, China

    Jianxin Wang

  2. Courant Institute, New York University, New York, New York, USA

    Chee Yap

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Fürer, M. (2015). Efficient Computation of the Characteristic Polynomial of a Threshold Graph. In: Wang, J., Yap, C. (eds) Frontiers in Algorithmics. FAW 2015. Lecture Notes in Computer Science(), vol 9130. Springer, Cham. https://doi.org/10.1007/978-3-319-19647-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-19647-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19646-6

  • Online ISBN: 978-3-319-19647-3

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