Constructive characterizations concerning weak Roman domination in trees
Given a graph G, we consider γr(G), γ{R2}(G), γr2(G) and γR(G) as the weak Roman domination number, the Roman {2}-domination number, the 2-rainbow domination number and the Roman domination number of G, respectively. It is known that γr(G)≤γ{R2}(G)≤γr2(G)≤γR(G) holds for any graph G. In connection w...
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| Veröffentlicht in: | Discrete Applied Mathematics 2020-09, Vol.284, p.384-390 |
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| creator | Cabrera-Martínez, Abel Yero, Ismael G. |
| description | Given a graph G, we consider γr(G), γ{R2}(G), γr2(G) and γR(G) as the weak Roman domination number, the Roman {2}-domination number, the 2-rainbow domination number and the Roman domination number of G, respectively.
It is known that γr(G)≤γ{R2}(G)≤γr2(G)≤γR(G) holds for any graph G. In connection with this, constructive characterizations of the trees T that satisfy the equalities above that are related with the weak Roman domination number are given in this work. That is, the trees T for which γr(T)=γ{R2}(T), γr(T)=γr2(T) and γr(T)=γR(T) are described. |
| doi_str_mv | 10.1016/j.dam.2020.03.058 |
| format | Article |
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It is known that γr(G)≤γ{R2}(G)≤γr2(G)≤γR(G) holds for any graph G. In connection with this, constructive characterizations of the trees T that satisfy the equalities above that are related with the weak Roman domination number are given in this work. That is, the trees T for which γr(T)=γ{R2}(T), γr(T)=γr2(T) and γr(T)=γR(T) are described.</description><identifier>ISSN: 0166-218X</identifier><identifier>EISSN: 1872-6771</identifier><identifier>DOI: 10.1016/j.dam.2020.03.058</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>2-rainbow domination ; Roman [formula omitted]-domination ; Roman domination ; Tree ; Trees ; Weak Roman domination</subject><ispartof>Discrete Applied Mathematics, 2020-09, Vol.284, p.384-390</ispartof><rights>2020 Elsevier B.V.</rights><rights>Copyright Elsevier BV Sep 30, 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-c4ab10386d3197b1b8aba58aba0f32b4581307abc15ee012df32445f01fbe4d53</citedby><cites>FETCH-LOGICAL-c325t-c4ab10386d3197b1b8aba58aba0f32b4581307abc15ee012df32445f01fbe4d53</cites><orcidid>0000-0003-2806-4842 ; 0000-0002-1619-1572</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.dam.2020.03.058$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Cabrera-Martínez, Abel</creatorcontrib><creatorcontrib>Yero, Ismael G.</creatorcontrib><title>Constructive characterizations concerning weak Roman domination in trees</title><title>Discrete Applied Mathematics</title><description>Given a graph G, we consider γr(G), γ{R2}(G), γr2(G) and γR(G) as the weak Roman domination number, the Roman {2}-domination number, the 2-rainbow domination number and the Roman domination number of G, respectively.
It is known that γr(G)≤γ{R2}(G)≤γr2(G)≤γR(G) holds for any graph G. In connection with this, constructive characterizations of the trees T that satisfy the equalities above that are related with the weak Roman domination number are given in this work. That is, the trees T for which γr(T)=γ{R2}(T), γr(T)=γr2(T) and γr(T)=γR(T) are described.</description><subject>2-rainbow domination</subject><subject>Roman [formula omitted]-domination</subject><subject>Roman domination</subject><subject>Tree</subject><subject>Trees</subject><subject>Weak Roman domination</subject><issn>0166-218X</issn><issn>1872-6771</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9UE1PwzAMjRBIjMEP4FaJc4vdtE0nTmjiS5qEhEDiFqWpCyksGUk2BL-ejHHmYsv2e_bzY-wUoUDA5nwserUsSiihAF5A3e6xCbaizBshcJ9NEqbJS2yfD9lRCCMAYKom7HbubIh-raPZUKZflVc6kjffKpo0ybSzmrw19iX7JPWWPbilslnvlsb-IjJjs-iJwjE7GNR7oJO_PGVP11eP89t8cX9zN79c5JqXdcx1pToE3jY9x5nosGtVp-ptgIGXXVW3yEGoTmNNlDT2qVtV9QA4dFT1NZ-ys93elXcfawpRjm7tbTopy0o0nAsxqxIKdyjtXQieBrnyZqn8l0SQW8PkKJNhcmuYBC6TYYlzseNQkr8x5GXQhtL7vfGko-yd-Yf9A0fUdAk</recordid><startdate>20200930</startdate><enddate>20200930</enddate><creator>Cabrera-Martínez, Abel</creator><creator>Yero, Ismael G.</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-2806-4842</orcidid><orcidid>https://orcid.org/0000-0002-1619-1572</orcidid></search><sort><creationdate>20200930</creationdate><title>Constructive characterizations concerning weak Roman domination in trees</title><author>Cabrera-Martínez, Abel ; Yero, Ismael G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-c4ab10386d3197b1b8aba58aba0f32b4581307abc15ee012df32445f01fbe4d53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>2-rainbow domination</topic><topic>Roman [formula omitted]-domination</topic><topic>Roman domination</topic><topic>Tree</topic><topic>Trees</topic><topic>Weak Roman domination</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cabrera-Martínez, Abel</creatorcontrib><creatorcontrib>Yero, Ismael G.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Discrete Applied Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cabrera-Martínez, Abel</au><au>Yero, Ismael G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Constructive characterizations concerning weak Roman domination in trees</atitle><jtitle>Discrete Applied Mathematics</jtitle><date>2020-09-30</date><risdate>2020</risdate><volume>284</volume><spage>384</spage><epage>390</epage><pages>384-390</pages><issn>0166-218X</issn><eissn>1872-6771</eissn><abstract>Given a graph G, we consider γr(G), γ{R2}(G), γr2(G) and γR(G) as the weak Roman domination number, the Roman {2}-domination number, the 2-rainbow domination number and the Roman domination number of G, respectively.
It is known that γr(G)≤γ{R2}(G)≤γr2(G)≤γR(G) holds for any graph G. In connection with this, constructive characterizations of the trees T that satisfy the equalities above that are related with the weak Roman domination number are given in this work. That is, the trees T for which γr(T)=γ{R2}(T), γr(T)=γr2(T) and γr(T)=γR(T) are described.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.dam.2020.03.058</doi><tpages>7</tpages><orcidid>https://orcid.org/0000-0003-2806-4842</orcidid><orcidid>https://orcid.org/0000-0002-1619-1572</orcidid></addata></record> |
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| subjects | 2-rainbow domination Roman [formula omitted]-domination Roman domination Tree Trees Weak Roman domination |
| title | Constructive characterizations concerning weak Roman domination in trees |
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