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http://hdl.handle.net/10198/17357| Title: | Efficient domination through eigenvalues |
| Author: | Cardoso, Domingos M. Lozin, Vadim V. Luz, Carlos J. Pacheco, Maria F. |
| Keywords: | (k,τ)-regular sets graph eigenvalue dominating induced matching efficient dominating set |
| Issue Date: | 2016 |
| Publisher: | Elsevier |
| Citation: | Cardoso, Domingos M.; Lozin, Vadim V.; Luz, Carlos J.; Pacheco, Maria F. (2016). Efficient domination through eigenvalues. Discrete Applied Mathematics. ISSN 0166-218X. 214, p. 54-62 |
| Abstract: | The paper begins with a new characterization of (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)-regular set. When τ = 1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NP- complete. If −1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it doesn’t work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs. |
| Peer review: | yes |
| URI: | http://hdl.handle.net/10198/17357 |
| DOI: | 10.1016/j.dam.2016.06.014 |
| ISSN: | 0166-218X |
| Appears in Collections: | ESTiG - Artigos em Revistas Indexados à WoS/Scopus |
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