On the General Position Numbers of Maximal Outerplane Graphs
A set R ⊆ V ( G ) of a graph G is a general position set if any triple set R 0 of R is non-geodesic, that is, no vertex of R 0 lies on any geodesic between the other two vertices of R 0 in G . Let R be the set of general position sets of a graph G . The general position number gp ( G ) of a graph G...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2023-11, Vol.46 (6), Article 198 |
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| container_title | Bulletin of the Malaysian Mathematical Sciences Society |
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| creator | Tian, Jing Xu, Kexiang Chao, Daikun |
| description | A set
R
⊆
V
(
G
)
of a graph
G
is a general position set if any triple set
R
0
of
R
is non-geodesic, that is, no vertex of
R
0
lies on any geodesic between the other two vertices of
R
0
in
G
. Let
R
be the set of general position sets of a graph
G
. The general position number
gp
(
G
)
of a graph
G
is defined as
gp
(
G
)
=
max
{
|
R
|
:
R
∈
R
}
. In this paper, for an arbitrary maximal outerplane graph
G
of order at least 7, we prove that
gp
(
G
)
=
3
if and only if
G
is a straight linear 2-tree. Moreover, we determine the upper bound on the gp-numbers for any maximal outerplane graph and characterize the corresponding extremal graphs. |
| doi_str_mv | 10.1007/s40840-023-01592-1 |
| format | Article |
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R
⊆
V
(
G
)
of a graph
G
is a general position set if any triple set
R
0
of
R
is non-geodesic, that is, no vertex of
R
0
lies on any geodesic between the other two vertices of
R
0
in
G
. Let
R
be the set of general position sets of a graph
G
. The general position number
gp
(
G
)
of a graph
G
is defined as
gp
(
G
)
=
max
{
|
R
|
:
R
∈
R
}
. In this paper, for an arbitrary maximal outerplane graph
G
of order at least 7, we prove that
gp
(
G
)
=
3
if and only if
G
is a straight linear 2-tree. Moreover, we determine the upper bound on the gp-numbers for any maximal outerplane graph and characterize the corresponding extremal graphs.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-023-01592-1</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Apexes ; Applications of Mathematics ; Graphs ; Mathematics ; Mathematics and Statistics ; Upper bounds</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2023-11, Vol.46 (6), Article 198</ispartof><rights>The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-14fa613f8ce21a8cf927c8c1a543b1ff82f20f137cc2a089f560e3d62055d7083</cites><orcidid>0000-0002-9376-5226</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40840-023-01592-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40840-023-01592-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Tian, Jing</creatorcontrib><creatorcontrib>Xu, Kexiang</creatorcontrib><creatorcontrib>Chao, Daikun</creatorcontrib><title>On the General Position Numbers of Maximal Outerplane Graphs</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>A set
R
⊆
V
(
G
)
of a graph
G
is a general position set if any triple set
R
0
of
R
is non-geodesic, that is, no vertex of
R
0
lies on any geodesic between the other two vertices of
R
0
in
G
. Let
R
be the set of general position sets of a graph
G
. The general position number
gp
(
G
)
of a graph
G
is defined as
gp
(
G
)
=
max
{
|
R
|
:
R
∈
R
}
. In this paper, for an arbitrary maximal outerplane graph
G
of order at least 7, we prove that
gp
(
G
)
=
3
if and only if
G
is a straight linear 2-tree. Moreover, we determine the upper bound on the gp-numbers for any maximal outerplane graph and characterize the corresponding extremal graphs.</description><subject>Apexes</subject><subject>Applications of Mathematics</subject><subject>Graphs</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Upper bounds</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWGr_gKcFz9GZ2c1HwYsUrUK1HvQc0jSxLe3umuyC_nujK3hzLnOY550ZHsbOES4RQF2lCnQFHKjkgGJKHI_YiFADrwjkMRsBkuRSgThlk5R2kEtIkoQjdr2si27ji7mvfbT74rlJ227b1MVTf1j5mIomFI_2Y3vIs2Xf-djubZ3xaNtNOmMnwe6Tn_z2MXu9u32Z3fPFcv4wu1lwRwo6jlWwEsugnSe02oUpKacdWlGVKwxBUyAIWCrnyIKeBiHBl2tJIMRagS7H7GLY28bmvfepM7umj3U-aUgrNRVag8gUDZSLTUrRB9PG_Hf8NAjmW5QZRJksyvyIMphD5RBKGa7ffPxb_U_qC9DraTY</recordid><startdate>20231101</startdate><enddate>20231101</enddate><creator>Tian, Jing</creator><creator>Xu, Kexiang</creator><creator>Chao, Daikun</creator><general>Springer Nature Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9376-5226</orcidid></search><sort><creationdate>20231101</creationdate><title>On the General Position Numbers of Maximal Outerplane Graphs</title><author>Tian, Jing ; Xu, Kexiang ; Chao, Daikun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-14fa613f8ce21a8cf927c8c1a543b1ff82f20f137cc2a089f560e3d62055d7083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Apexes</topic><topic>Applications of Mathematics</topic><topic>Graphs</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tian, Jing</creatorcontrib><creatorcontrib>Xu, Kexiang</creatorcontrib><creatorcontrib>Chao, Daikun</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tian, Jing</au><au>Xu, Kexiang</au><au>Chao, Daikun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the General Position Numbers of Maximal Outerplane Graphs</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2023-11-01</date><risdate>2023</risdate><volume>46</volume><issue>6</issue><artnum>198</artnum><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>A set
R
⊆
V
(
G
)
of a graph
G
is a general position set if any triple set
R
0
of
R
is non-geodesic, that is, no vertex of
R
0
lies on any geodesic between the other two vertices of
R
0
in
G
. Let
R
be the set of general position sets of a graph
G
. The general position number
gp
(
G
)
of a graph
G
is defined as
gp
(
G
)
=
max
{
|
R
|
:
R
∈
R
}
. In this paper, for an arbitrary maximal outerplane graph
G
of order at least 7, we prove that
gp
(
G
)
=
3
if and only if
G
is a straight linear 2-tree. Moreover, we determine the upper bound on the gp-numbers for any maximal outerplane graph and characterize the corresponding extremal graphs.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s40840-023-01592-1</doi><orcidid>https://orcid.org/0000-0002-9376-5226</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0126-6705 |
| ispartof | Bulletin of the Malaysian Mathematical Sciences Society, 2023-11, Vol.46 (6), Article 198 |
| issn | 0126-6705 2180-4206 |
| language | eng |
| recordid | cdi_proquest_journals_2877958805 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Apexes Applications of Mathematics Graphs Mathematics Mathematics and Statistics Upper bounds |
| title | On the General Position Numbers of Maximal Outerplane Graphs |
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