Bród, Dorota and Skupień, Zdzis\law - Recurrence among trees with most numerous efficient dominating sets

dmtcs:445 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, Vol. 10 no. 1
Recurrence among trees with most numerous efficient dominating sets

Authors: Bród, Dorota and Skupień, Zdzis\law

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 is exponential. Also the number of maximum n-vertex trees is shown to be bounded below by an increasing exponential function in n.


Source : oai:HAL:hal-00972308v1
Volume: Vol. 10 no. 1
Section: Graph and Algorithms
Published on: January 1, 2008
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


Share

Browsing statistics

This page has been seen 31 times.
This article's PDF has been downloaded 73 times.