%0 Journal Article
%T Recurrence among trees with most numerous efficient dominating sets
%A Dorota Br¨®d
%A ZdzisŁżaw Skupie¨˝
%J Discrete Mathematics & Theoretical Computer Science
%D 2008
%I Discrete Mathematics & Theoretical Computer Science
%X A dominating set D of vertices in a graph G is called an efficient dominating set if the distance between any two vertices in D is at least three. A tree T of order n is called maximum if T has the largest number of efficient dominating sets among all n-vertex trees. A constructive characterization of all maximum trees is given. Their structure has recurring aspects with period 7. Moreover, the number of efficient dominating sets in maximum n-vertex trees is determined and appears to be exponential. Also the number of maximum n-vertex trees is shown to be bounded below by an increasing exponential function in n.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/610