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Locating-coloring on Halin graphs with a certain number of inner faces
For any tree T with at least four vertices and no vertices of degree two, define a Halin graph H(T) as a planar graph constructed from an embedding of T in a plane by connecting all the leaves (the vertices of degree 1) of T to form a cycle C that passes around T in the natural cyclic order defined...
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| creator | Purwasih, I. A. Baskoro, E. T. Assiyatun, H. Suprijanto, D. |
| description | For any tree T with at least four vertices and no vertices of degree two, define a Halin graph H(T) as a planar graph constructed from an embedding of T in a plane by connecting all the leaves (the vertices of degree 1) of T to form a cycle C that passes around T in the natural cyclic order defined by the embedding of T . The study of the properties of a Halin graph has received much attention. For instances, it has been shown that every Halin graph is 3-connected and Hamiltonian. A Halin graph has also treewidth at most three, so that many graph optimization problems that are NP-complete for arbitrary planar graphs may be solved in linear time on Halin graphs using dynamic programming. In this paper, we characterize all Halin graphs with 3,4,5,6, and 7 inner faces and give their locating-chromatic number. Furthermore, we show that there exist a Halin graph having locating-chromatic number k ≥ 4 with
r
≥
max
{
3
,
(
k
−
2
)
3
−
(
k
−
2
)
2
2
+
1
}
inner faces. |
| doi_str_mv | 10.1063/1.4940815 |
| format | conference_proceeding |
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r
≥
max
{
3
,
(
k
−
2
)
3
−
(
k
−
2
)
2
2
+
1
}
inner faces.</description><identifier>ISSN: 0094-243X</identifier><identifier>EISSN: 1551-7616</identifier><identifier>DOI: 10.1063/1.4940815</identifier><identifier>CODEN: APCPCS</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Coloring ; Construction planning ; Dynamic programming ; Embedding ; Graph theory ; Graphs</subject><ispartof>AIP Conference Proceedings, 2016, Vol.1707 (1)</ispartof><rights>AIP Publishing LLC</rights><rights>2016 AIP Publishing LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,27924,27925</link.rule.ids></links><search><contributor>Kusumo, Fajar Adi</contributor><contributor>Susanti, Yeni</contributor><contributor>Aluicius, Irwan Endrayanto</contributor><contributor>Wijayanti, Indah Emilia</contributor><creatorcontrib>Purwasih, I. A.</creatorcontrib><creatorcontrib>Baskoro, E. T.</creatorcontrib><creatorcontrib>Assiyatun, H.</creatorcontrib><creatorcontrib>Suprijanto, D.</creatorcontrib><title>Locating-coloring on Halin graphs with a certain number of inner faces</title><title>AIP Conference Proceedings</title><description>For any tree T with at least four vertices and no vertices of degree two, define a Halin graph H(T) as a planar graph constructed from an embedding of T in a plane by connecting all the leaves (the vertices of degree 1) of T to form a cycle C that passes around T in the natural cyclic order defined by the embedding of T . The study of the properties of a Halin graph has received much attention. For instances, it has been shown that every Halin graph is 3-connected and Hamiltonian. A Halin graph has also treewidth at most three, so that many graph optimization problems that are NP-complete for arbitrary planar graphs may be solved in linear time on Halin graphs using dynamic programming. In this paper, we characterize all Halin graphs with 3,4,5,6, and 7 inner faces and give their locating-chromatic number. Furthermore, we show that there exist a Halin graph having locating-chromatic number k ≥ 4 with
r
≥
max
{
3
,
(
k
−
2
)
3
−
(
k
−
2
)
2
2
+
1
}
inner faces.</description><subject>Coloring</subject><subject>Construction planning</subject><subject>Dynamic programming</subject><subject>Embedding</subject><subject>Graph theory</subject><subject>Graphs</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2016</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNp9kE9LAzEUxIMoWKsHv0HAm7D1vfzZ3RylWCsUvCh4CzGbtFvaZE12Fb-9Ky148_SGx48ZZgi5RpghlPwOZ0IJqFGekAlKiUVVYnlKJgBKFEzwt3NykfMWgKmqqidksYrW9G1YFzbuYhoFjYEuza4NdJ1Mt8n0q-031FDrUm_Gbxj27y7R6Gkbwii8sS5fkjNvdtldHe-UvC4eXubLYvX8-DS_XxUdk7wvhKyVZcIges8EA1OKqnSmkbVv0IJn3vFSIEdslPGVZ9wa51F4AFFZEHxKbg6-XYofg8u93sYhhTFSM2SokCshR-r2QGXb9mO7GHSX2r1J3xpB_-6kUR93-g_-jOkP1F3j-Q-ktWfH</recordid><startdate>20160211</startdate><enddate>20160211</enddate><creator>Purwasih, I. A.</creator><creator>Baskoro, E. T.</creator><creator>Assiyatun, H.</creator><creator>Suprijanto, D.</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20160211</creationdate><title>Locating-coloring on Halin graphs with a certain number of inner faces</title><author>Purwasih, I. A. ; Baskoro, E. T. ; Assiyatun, H. ; Suprijanto, D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p253t-4589c24a11ff2420a6476ead58fd1c0f2fe3641311d9af7f23caef14f0047c043</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Coloring</topic><topic>Construction planning</topic><topic>Dynamic programming</topic><topic>Embedding</topic><topic>Graph theory</topic><topic>Graphs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Purwasih, I. A.</creatorcontrib><creatorcontrib>Baskoro, E. T.</creatorcontrib><creatorcontrib>Assiyatun, H.</creatorcontrib><creatorcontrib>Suprijanto, D.</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Purwasih, I. A.</au><au>Baskoro, E. T.</au><au>Assiyatun, H.</au><au>Suprijanto, D.</au><au>Kusumo, Fajar Adi</au><au>Susanti, Yeni</au><au>Aluicius, Irwan Endrayanto</au><au>Wijayanti, Indah Emilia</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Locating-coloring on Halin graphs with a certain number of inner faces</atitle><btitle>AIP Conference Proceedings</btitle><date>2016-02-11</date><risdate>2016</risdate><volume>1707</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>For any tree T with at least four vertices and no vertices of degree two, define a Halin graph H(T) as a planar graph constructed from an embedding of T in a plane by connecting all the leaves (the vertices of degree 1) of T to form a cycle C that passes around T in the natural cyclic order defined by the embedding of T . The study of the properties of a Halin graph has received much attention. For instances, it has been shown that every Halin graph is 3-connected and Hamiltonian. A Halin graph has also treewidth at most three, so that many graph optimization problems that are NP-complete for arbitrary planar graphs may be solved in linear time on Halin graphs using dynamic programming. In this paper, we characterize all Halin graphs with 3,4,5,6, and 7 inner faces and give their locating-chromatic number. Furthermore, we show that there exist a Halin graph having locating-chromatic number k ≥ 4 with
r
≥
max
{
3
,
(
k
−
2
)
3
−
(
k
−
2
)
2
2
+
1
}
inner faces.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4940815</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0094-243X |
| ispartof | AIP Conference Proceedings, 2016, Vol.1707 (1) |
| issn | 0094-243X 1551-7616 |
| language | eng |
| recordid | cdi_proquest_journals_2121913945 |
| source | American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list) |
| subjects | Coloring Construction planning Dynamic programming Embedding Graph theory Graphs |
| title | Locating-coloring on Halin graphs with a certain number of inner faces |
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