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On Efficiently Total Dominatable Digraphs

On Efficiently Total Dominatable Digraphs An efficient total dominating set is an important property in the design of network interconnection. An efficient total dominating set S of a digraph D is a vertex subset such that every vertex of D has exactly one predecessor. If D has an efficient total dominating set, then D is called an efficiently total dominatable digraph. Let $$\textit{EDT}$$ EDT denote the decision problem associated to the existence of efficient total dominating sets. It is known that $$\textit{ETD}$$ ETD is NP-complete on the orientations of chordal graphs. In this paper, we give a characterization on block graphs having an efficiently total dominatable orientation. This characterization implies polynomial solvability of the $$\textit{ETD}$$ ETD on the orientations of block graphs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

On Efficiently Total Dominatable Digraphs

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-016-0424-1
Publisher site
See Article on Publisher Site

Abstract

An efficient total dominating set is an important property in the design of network interconnection. An efficient total dominating set S of a digraph D is a vertex subset such that every vertex of D has exactly one predecessor. If D has an efficient total dominating set, then D is called an efficiently total dominatable digraph. Let $$\textit{EDT}$$ EDT denote the decision problem associated to the existence of efficient total dominating sets. It is known that $$\textit{ETD}$$ ETD is NP-complete on the orientations of chordal graphs. In this paper, we give a characterization on block graphs having an efficiently total dominatable orientation. This characterization implies polynomial solvability of the $$\textit{ETD}$$ ETD on the orientations of block graphs.

Journal

Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals

Published: Sep 30, 2016

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