Efficient computation of the characteristic polynomial of a threshold graph

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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
StatePublished - Jan 2 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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