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Title: Efficient domination through eigenvalues
Author: Cardoso, Domingos M.
Lozin, V. V.
Luz, C. J.
Pacheco, M. F.
Keywords: Efficient dominating set
Dominating induced matching
(k,τ)(k,τ)-regular sets
Graph eigenvalue
Issue Date: 11-Dec-2016
Publisher: Elsevier
Abstract: The paper begins with a new characterization of (k,τ)(k,τ)-regular sets. Then, using this result as well as the theory of star complements, we derive a simplex-like algorithm for determining whether or not a graph contains a (0,τ)(0,τ)-regular set. When τ=1τ=1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NP-complete. If −1−1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it does not work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs.
Peer review: yes
DOI: 10.1016/j.dam.2016.06.014
ISSN: 0166-218X
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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