Journal of Combinatorial Optimization

, Volume 31, Issue 3, pp 1134–1141 | Cite as

On the efficiency index of a graph

  • Rommel Barbosa
  • Peter Slater


A graph \(G\) has an efficient dominating set \(D \subseteq V(G)\) if \(D\) dominates every vertex exactly once. In this paper we introduce the study of the family \({S_k}\) of graphs for which every \(G-S\) is efficiently dominatable for \(0 \le |S|\le k\). Assuming that \(G\) is efficiently dominatable, the efficiency index is the largest value k for which \(G\) is in \(S_k\). A graph \(G\) will be called super-efficient if every induced subgraph is efficiently dominatable. We give some characterizations for trees, grids, cylinders and torii to be super-efficient.


Dominating sets Grids Cylinders Torii 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Instituto de InformaticaUniversidade Federal de GoiasGoiâniaBrazil
  2. 2.Department of Computer Science and Department of Mathematical SciencesUniversity of AlabamaHuntsvilleUSA

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