Efficient computation of the characteristic polynomial of a threshold graph

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    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

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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