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Efficient Computation of the Characteristic Polynomial of a Threshold Graph
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