A lower bound on the double outer-independent domination number of a tree
A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph is a set of vertices of such that every vertex of is dominated by at least two vertices of , and the set ( ) \ is independent. The double outer-independent domination number...
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| Veröffentlicht in: | Demonstratio mathematica 2012-03, Vol.45 (1), p.17-23 |
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| container_title | Demonstratio mathematica |
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| creator | Krzywkowski, Marcin |
| description | A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph
is a set
of vertices of
such that every vertex of
is dominated by at least two vertices of
, and the set
(
) \
is independent. The double outer-independent domination number of a graph
, denoted by
, is the minimum cardinality of a double outer-independent dominating set of
. We prove that for every nontrivial tree
of order
, with
leaves and
support vertices we have
, and we characterize the trees attaining this lower bound. We also give a constructive characterization of trees
such that |
| doi_str_mv | 10.1515/dema-2013-0358 |
| format | Article |
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is a set
of vertices of
such that every vertex of
is dominated by at least two vertices of
, and the set
(
) \
is independent. The double outer-independent domination number of a graph
, denoted by
, is the minimum cardinality of a double outer-independent dominating set of
. We prove that for every nontrivial tree
of order
, with
leaves and
support vertices we have
, and we characterize the trees attaining this lower bound. We also give a constructive characterization of trees
such that</description><identifier>ISSN: 2391-4661</identifier><identifier>EISSN: 2391-4661</identifier><identifier>DOI: 10.1515/dema-2013-0358</identifier><language>eng</language><publisher>De Gruyter Open</publisher><subject>05C05 ; 05C69 ; double domination ; double outer-independent domination ; tree</subject><ispartof>Demonstratio mathematica, 2012-03, Vol.45 (1), p.17-23</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,864,27923,27924</link.rule.ids></links><search><creatorcontrib>Krzywkowski, Marcin</creatorcontrib><title>A lower bound on the double outer-independent domination number of a tree</title><title>Demonstratio mathematica</title><description>A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph
is a set
of vertices of
such that every vertex of
is dominated by at least two vertices of
, and the set
(
) \
is independent. The double outer-independent domination number of a graph
, denoted by
, is the minimum cardinality of a double outer-independent dominating set of
. We prove that for every nontrivial tree
of order
, with
leaves and
support vertices we have
, and we characterize the trees attaining this lower bound. We also give a constructive characterization of trees
such that</description><subject>05C05</subject><subject>05C69</subject><subject>double domination</subject><subject>double outer-independent domination</subject><subject>tree</subject><issn>2391-4661</issn><issn>2391-4661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp1kE1rwzAMhs3YYKXrdWf_AXf-jsNOpeyjUNhlOxsnVraUxC5OQum_n0N36GU6SC9Ir5AehB4ZXTPF1JOH3hFOmSBUKHODFlyUjEit2e2VvkerYTjQHNpIzekC7Ta4iydIuIpT8DgGPP4A9nGqOsBxGiGRNng4Qk5hzI2-DW5s81yY-ir7YoMdHhPAA7prXDfA6q8u0dfry-f2new_3nbbzZ7U3OiRGCeFloZrUKVk3gnNpeOmqakvawmgoBKNoF4UvGKq8FTSWpR1U0ClGRNeLNH6srdOcRgSNPaY2t6ls2XUzizszMLOLOzMIhueL4aT6_I_Hr7TdM7CHuKUQj71H6NUjBXiF3mGZYw</recordid><startdate>20120301</startdate><enddate>20120301</enddate><creator>Krzywkowski, Marcin</creator><general>De Gruyter Open</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20120301</creationdate><title>A lower bound on the double outer-independent domination number of a tree</title><author>Krzywkowski, Marcin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c286t-8a4364826e5941da3624a28fc0d9c4ee5eb3f30d372b157d040c39cf7eb6113d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>05C05</topic><topic>05C69</topic><topic>double domination</topic><topic>double outer-independent domination</topic><topic>tree</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Krzywkowski, Marcin</creatorcontrib><collection>CrossRef</collection><jtitle>Demonstratio mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krzywkowski, Marcin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A lower bound on the double outer-independent domination number of a tree</atitle><jtitle>Demonstratio mathematica</jtitle><date>2012-03-01</date><risdate>2012</risdate><volume>45</volume><issue>1</issue><spage>17</spage><epage>23</epage><pages>17-23</pages><issn>2391-4661</issn><eissn>2391-4661</eissn><abstract>A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph
is a set
of vertices of
such that every vertex of
is dominated by at least two vertices of
, and the set
(
) \
is independent. The double outer-independent domination number of a graph
, denoted by
, is the minimum cardinality of a double outer-independent dominating set of
. We prove that for every nontrivial tree
of order
, with
leaves and
support vertices we have
, and we characterize the trees attaining this lower bound. We also give a constructive characterization of trees
such that</abstract><pub>De Gruyter Open</pub><doi>10.1515/dema-2013-0358</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Demonstratio mathematica, 2012-03, Vol.45 (1), p.17-23 |
| issn | 2391-4661 2391-4661 |
| language | eng |
| recordid | cdi_crossref_primary_10_1515_dema_2013_0358 |
| source | DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection |
| subjects | 05C05 05C69 double domination double outer-independent domination tree |
| title | A lower bound on the double outer-independent domination number of a tree |
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