Skip to Main content Skip to Navigation
Journal articles

Recurrence among trees with most numerous efficient dominating sets

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download

https://hal.inria.fr/hal-00972308
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Thursday, April 3, 2014 - 4:07:46 PM
Last modification on : Tuesday, December 17, 2019 - 5:48:02 PM
Long-term archiving on: : Thursday, July 3, 2014 - 4:30:51 PM

File

610-3174-1-PB.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00972308, version 1

Collections

Citation

Dorota Bród, Zdzis\law Skupień. Recurrence among trees with most numerous efficient dominating sets. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, 10 (1), pp.43--55. ⟨hal-00972308⟩

Share

Metrics

Record views

268

Files downloads

828