Distance paired domination numbers of graphs |
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Authors: | Joanna Raczek |
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Affiliation: | Department of Discrete Mathematics, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland |
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Abstract: | In this paper, we study a generalization of the paired domination number. Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The k-distance paired domination number is the cardinality of a smallest k-distance paired dominating set of G. We investigate properties of the k-distance paired domination number of a graph. We also give an upper bound and a lower bound on the k-distance paired domination number of a non-trivial tree T in terms of the size of T and the number of leaves in T and we also characterize the extremal trees. |
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Keywords: | 05C05 05C69 |
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