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Bipartite Theory of Graphs: Outer-Independent Domination
Let G = ( V , E ) be a bipartite graph with partite sets X and Y . Two vertices of X are X -adjacent if they have a common neighbor in Y , and they are X -independent otherwise. A subset D ⊆ X is an X -outer-independent dominating set of G if every vertex of X \ D has an X -neighbor in D , and all v...
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| Published in: | National Academy science letters 2015-04, Vol.38 (2), p.169-172 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| Citations: | Items that cite this one |
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| cited_by | cdi_FETCH-LOGICAL-c288t-14c33689ac5e32b5011caeae2e112881588d56c23d084d08f954def284caf8983 |
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| container_end_page | 172 |
| container_issue | 2 |
| container_start_page | 169 |
| container_title | National Academy science letters |
| container_volume | 38 |
| creator | Krzywkowski, Marcin Venkatakrishnan, Yanamandram B. |
| description | Let
G
=
(
V
,
E
)
be a bipartite graph with partite sets
X
and
Y
. Two vertices of
X
are
X
-adjacent if they have a common neighbor in
Y
, and they are
X
-independent otherwise. A subset
D
⊆
X
is an
X
-outer-independent dominating set of
G
if every vertex of
X
\
D
has an
X
-neighbor in
D
, and all vertices of
X
\
D
are pairwise
X
-independent. The
X
-outer-independent domination number of
G
, denoted by
γ
X
o
i
(
G
)
, is the minimum cardinality of an
X
-outer-independent dominating set of
G
. We prove several properties and bounds on the number
γ
X
o
i
(
G
)
. |
| doi_str_mv | 10.1007/s40009-014-0315-7 |
| format | article |
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G
=
(
V
,
E
)
be a bipartite graph with partite sets
X
and
Y
. Two vertices of
X
are
X
-adjacent if they have a common neighbor in
Y
, and they are
X
-independent otherwise. A subset
D
⊆
X
is an
X
-outer-independent dominating set of
G
if every vertex of
X
\
D
has an
X
-neighbor in
D
, and all vertices of
X
\
D
are pairwise
X
-independent. The
X
-outer-independent domination number of
G
, denoted by
γ
X
o
i
(
G
)
, is the minimum cardinality of an
X
-outer-independent dominating set of
G
. We prove several properties and bounds on the number
γ
X
o
i
(
G
)
.</description><identifier>ISSN: 0250-541X</identifier><identifier>EISSN: 2250-1754</identifier><identifier>DOI: 10.1007/s40009-014-0315-7</identifier><language>eng</language><publisher>India: Springer India</publisher><subject>History of Science ; Humanities and Social Sciences ; multidisciplinary ; Science ; Science (multidisciplinary) ; Short Communication</subject><ispartof>National Academy science letters, 2015-04, Vol.38 (2), p.169-172</ispartof><rights>The National Academy of Sciences, India 2014</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-14c33689ac5e32b5011caeae2e112881588d56c23d084d08f954def284caf8983</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids></links><search><creatorcontrib>Krzywkowski, Marcin</creatorcontrib><creatorcontrib>Venkatakrishnan, Yanamandram B.</creatorcontrib><title>Bipartite Theory of Graphs: Outer-Independent Domination</title><title>National Academy science letters</title><addtitle>Natl. Acad. Sci. Lett</addtitle><description>Let
G
=
(
V
,
E
)
be a bipartite graph with partite sets
X
and
Y
. Two vertices of
X
are
X
-adjacent if they have a common neighbor in
Y
, and they are
X
-independent otherwise. A subset
D
⊆
X
is an
X
-outer-independent dominating set of
G
if every vertex of
X
\
D
has an
X
-neighbor in
D
, and all vertices of
X
\
D
are pairwise
X
-independent. The
X
-outer-independent domination number of
G
, denoted by
γ
X
o
i
(
G
)
, is the minimum cardinality of an
X
-outer-independent dominating set of
G
. We prove several properties and bounds on the number
γ
X
o
i
(
G
)
.</description><subject>History of Science</subject><subject>Humanities and Social Sciences</subject><subject>multidisciplinary</subject><subject>Science</subject><subject>Science (multidisciplinary)</subject><subject>Short Communication</subject><issn>0250-541X</issn><issn>2250-1754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9j79OwzAQhy0EElHpA7DlBQx3jp04bFCgVKrUpUhslnEuNBVNItsd-va4SmeG-zN8v9N9jN0jPCBA9RgkANQcUHIoUPHqimVCKOBYKXnNMjjvSuLXLZuHsE8wqFIpFBnTL91ofewi5dsdDf6UD22-9Hbchad8c4zk-apvaKTU-pi_Doeut7Eb-jt209rfQPPLnLHP97ft4oOvN8vV4nnNndA6cpSuKEpdW6eoEN8KEJ0lS4IQE4BK60aVThQNaJmqrZVsqBVaOtvqWhczhtNd54cQPLVm9N3B-pNBMGd7M9mbZG_O9qZKGTFlQmL7H_JmPxx9n978J_QHYeRbuQ</recordid><startdate>20150401</startdate><enddate>20150401</enddate><creator>Krzywkowski, Marcin</creator><creator>Venkatakrishnan, Yanamandram B.</creator><general>Springer India</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150401</creationdate><title>Bipartite Theory of Graphs: Outer-Independent Domination</title><author>Krzywkowski, Marcin ; Venkatakrishnan, Yanamandram B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-14c33689ac5e32b5011caeae2e112881588d56c23d084d08f954def284caf8983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>History of Science</topic><topic>Humanities and Social Sciences</topic><topic>multidisciplinary</topic><topic>Science</topic><topic>Science (multidisciplinary)</topic><topic>Short Communication</topic><toplevel>online_resources</toplevel><creatorcontrib>Krzywkowski, Marcin</creatorcontrib><creatorcontrib>Venkatakrishnan, Yanamandram B.</creatorcontrib><collection>CrossRef</collection><jtitle>National Academy science letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krzywkowski, Marcin</au><au>Venkatakrishnan, Yanamandram B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bipartite Theory of Graphs: Outer-Independent Domination</atitle><jtitle>National Academy science letters</jtitle><stitle>Natl. Acad. Sci. Lett</stitle><date>2015-04-01</date><risdate>2015</risdate><volume>38</volume><issue>2</issue><spage>169</spage><epage>172</epage><pages>169-172</pages><issn>0250-541X</issn><eissn>2250-1754</eissn><abstract>Let
G
=
(
V
,
E
)
be a bipartite graph with partite sets
X
and
Y
. Two vertices of
X
are
X
-adjacent if they have a common neighbor in
Y
, and they are
X
-independent otherwise. A subset
D
⊆
X
is an
X
-outer-independent dominating set of
G
if every vertex of
X
\
D
has an
X
-neighbor in
D
, and all vertices of
X
\
D
are pairwise
X
-independent. The
X
-outer-independent domination number of
G
, denoted by
γ
X
o
i
(
G
)
, is the minimum cardinality of an
X
-outer-independent dominating set of
G
. We prove several properties and bounds on the number
γ
X
o
i
(
G
)
.</abstract><cop>India</cop><pub>Springer India</pub><doi>10.1007/s40009-014-0315-7</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0250-541X |
| ispartof | National Academy science letters, 2015-04, Vol.38 (2), p.169-172 |
| issn | 0250-541X 2250-1754 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s40009_014_0315_7 |
| source | Springer Nature |
| subjects | History of Science Humanities and Social Sciences multidisciplinary Science Science (multidisciplinary) Short Communication |
| title | Bipartite Theory of Graphs: Outer-Independent Domination |
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