Efficient computation of the characteristic polynomial of a threshold graph

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    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(nlog2⁡n) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time. We improve the running time drastically in the case where there is a small number of alternations between 0's and 1's in the sequence defining a threshold graph.

    Original languageEnglish (US)
    Pages (from-to)3-10
    Number of pages8
    JournalTheoretical Computer Science
    Volume657
    DOIs
    StatePublished - Jan 2 2017

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    Threshold Graph
    Characteristic polynomial
    Polynomials
    Hammers
    Vertex of a graph
    Clique-width
    Cographs
    Alternation
    Graph in graph theory
    Fast Algorithm
    Efficient Algorithms
    Adjacent
    Computing

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

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    title = "Efficient computation of the characteristic polynomial of a threshold graph",
    abstract = "An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph. Threshold graphs were introduced by Chv{\'a}tal 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(nlog2⁡n) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time. We improve the running time drastically in the case where there is a small number of alternations between 0's and 1's in the sequence defining a threshold graph.",
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    Efficient computation of the characteristic polynomial of a threshold graph. / Fürer, Martin.

    In: Theoretical Computer Science, Vol. 657, 02.01.2017, p. 3-10.

    Research output: Contribution to journalArticle

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