Lower bounds for the domination number

Ermelinda Delaviña; Ryan Pepper; Bill Waller

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 3, page 475-487
  • ISSN: 2083-5892

Abstract

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In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matching.

How to cite

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Ermelinda Delaviña, Ryan Pepper, and Bill Waller. "Lower bounds for the domination number." Discussiones Mathematicae Graph Theory 30.3 (2010): 475-487. <http://eudml.org/doc/270791>.

@article{ErmelindaDelaviña2010,
abstract = {In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matching.},
author = {Ermelinda Delaviña, Ryan Pepper, Bill Waller},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination number; radius; matching; cut-vertices},
language = {eng},
number = {3},
pages = {475-487},
title = {Lower bounds for the domination number},
url = {http://eudml.org/doc/270791},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Ermelinda Delaviña
AU - Ryan Pepper
AU - Bill Waller
TI - Lower bounds for the domination number
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 3
SP - 475
EP - 487
AB - In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matching.
LA - eng
KW - domination number; radius; matching; cut-vertices
UR - http://eudml.org/doc/270791
ER -

References

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