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 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}
}