On the efficiency index of a graph

Rommel Barbosa () and Peter Slater
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Rommel Barbosa: Universidade Federal de Goias
Peter Slater: University of Alabama

Journal of Combinatorial Optimization, 2016, vol. 31, issue 3, No 13, 1134-1141

Abstract: Abstract A graph $$G$$ G has an efficient dominating set $$D \subseteq V(G)$$ D ⊆ V ( G ) if $$D$$ D dominates every vertex exactly once. In this paper we introduce the study of the family $${S_k}$$ S k of graphs for which every $$G-S$$ G - S is efficiently dominatable for $$0 \le |S|\le k$$ 0 ≤ | S | ≤ k . Assuming that $$G$$ G is efficiently dominatable, the efficiency index is the largest value k for which $$G$$ G is in $$S_k$$ S k . A graph $$G$$ 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.

Keywords: Dominating sets; Grids; Cylinders; Torii (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9814-1

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