English

Efficient Computation of the Characteristic Polynomial of a Threshold Graph

Data Structures and Algorithms 2015-03-03 v1

Abstract

An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph. Threshold graphs were introduced by Chv\'atal 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(nlog2n)O(n \log^2 n) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time. Keywords: Efficient Algorithms, Threshold Graphs, Characteristic Polynomial.

Keywords

Cite

@article{arxiv.1503.00617,
  title  = {Efficient Computation of the Characteristic Polynomial of a Threshold Graph},
  author = {Martin Fürer},
  journal= {arXiv preprint arXiv:1503.00617},
  year   = {2015}
}
R2 v1 2026-06-22T08:42:07.057Z