Total restrained domination numbers of trees |
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Authors: | Joanna Raczek |
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Institution: | Department of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland |
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Abstract: | For a given connected graph G=(V,E), a set Dtr⊆V(G) is a total restrained dominating set if it is dominating and both 〈Dtr〉 and 〈V(G)-Dtr〉 do not contain isolate vertices. The cardinality of the minimum total restrained dominating set in G is the total restrained domination number and is denoted by γtr(G). In this paper we characterize the trees with equal total and total restrained dominating numbers and give a lower bound on the total restrained dominating number of a tree T in terms of its order and the number of leaves of T. |
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Keywords: | 05C05 05C69 |
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