Worst-case efficient dominating sets in digraphs

Details Worst-case efficient dominating sets in digraphs Worst-case efficient dominating sets in digraphs

2012-01-09

arxiv.org/abs/1201.1728v2

Mathematics

Combinatorics

11 pages, 3 figures

Scientific paper

Let $1\le n\in\Z$. {\it Worst-case efficient dominating sets in digraphs} are conceived so that their presence in certain strong digraphs $\vec{ST}_n$ corresponds to that of efficient dominating sets \cite{arum1,Hay} in star graphs $ST_n$ \cite{akers}: the fact that the star graphs $ST_n$ form a so-called dense segmental neighborly E-chain \cite{io} is reflected in a corresponding fact for the digraphs $\vec{ST}_n$. Related chains of graphs and open problems are presented as well.

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