Extremal Edge General Position Sets in Some Graphs
A set of edges X ⊆ E ( G ) of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number gp e ( G ) of G is the cardinality of a largest edge general position set in G . Graphs G with gp e ( G ) = | E ( G ) | - 1 and with gp e (...
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| Veröffentlicht in: | Graphs and combinatorics 2024-04, Vol.40 (2), Article 40 |
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| container_title | Graphs and combinatorics |
| container_volume | 40 |
| creator | Tian, Jing Klavžar, Sandi Tan, Elif |
| description | A set of edges
X
⊆
E
(
G
)
of a graph
G
is an edge general position set if no three edges from
X
lie on a common shortest path. The edge general position number
gp
e
(
G
)
of
G
is the cardinality of a largest edge general position set in
G
. Graphs
G
with
gp
e
(
G
)
=
|
E
(
G
)
|
-
1
and with
gp
e
(
G
)
=
3
are respectively characterized. Sharp upper and lower bounds on
gp
e
(
G
)
are proved for block graphs
G
and exact values are determined for several specific block graphs. |
| doi_str_mv | 10.1007/s00373-024-02770-z |
| format | Article |
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X
⊆
E
(
G
)
of a graph
G
is an edge general position set if no three edges from
X
lie on a common shortest path. The edge general position number
gp
e
(
G
)
of
G
is the cardinality of a largest edge general position set in
G
. Graphs
G
with
gp
e
(
G
)
=
|
E
(
G
)
|
-
1
and with
gp
e
(
G
)
=
3
are respectively characterized. Sharp upper and lower bounds on
gp
e
(
G
)
are proved for block graphs
G
and exact values are determined for several specific block graphs.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-024-02770-z</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Engineering Design ; Graph theory ; Graphs ; Lower bounds ; Mathematics ; Mathematics and Statistics ; Original Paper ; Shortest-path problems</subject><ispartof>Graphs and combinatorics, 2024-04, Vol.40 (2), Article 40</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-4809e634422c4402bbb572043f1bd1c98f71a099809cdb1e759c186d1909b143</citedby><cites>FETCH-LOGICAL-c363t-4809e634422c4402bbb572043f1bd1c98f71a099809cdb1e759c186d1909b143</cites><orcidid>0000-0002-1556-4744</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/s00373-024-02770-z$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-024-02770-z$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Tian, Jing</creatorcontrib><creatorcontrib>Klavžar, Sandi</creatorcontrib><creatorcontrib>Tan, Elif</creatorcontrib><title>Extremal Edge General Position Sets in Some Graphs</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>A set of edges
X
⊆
E
(
G
)
of a graph
G
is an edge general position set if no three edges from
X
lie on a common shortest path. The edge general position number
gp
e
(
G
)
of
G
is the cardinality of a largest edge general position set in
G
. Graphs
G
with
gp
e
(
G
)
=
|
E
(
G
)
|
-
1
and with
gp
e
(
G
)
=
3
are respectively characterized. Sharp upper and lower bounds on
gp
e
(
G
)
are proved for block graphs
G
and exact values are determined for several specific block graphs.</description><subject>Combinatorics</subject><subject>Engineering Design</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Lower bounds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Shortest-path problems</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kNFLwzAQxoMoWKf_gE8Fn6N3Sdo0jzLmJgwU3Hto03R2rE1NOtD99WZW8M2H4-O433d3fITcItwjgHwIAFxyCkzEkhLo8YwkKHhGM4XinCSgECkgqktyFcIOADIUkBC2-By97cp9uqi3Nl3a3vrYvLrQjq3r0zc7hrSN6ro49eXwHq7JRVPug7351RnZPC028xVdvyyf549ranjORyoKUDbnQjBmhABWVVUmGQjeYFWjUUUjsQSlImbqCq3MlMEir1GBquLrM3I3rR28-zjYMOqdO_g-XtRMFZIhU_mJYhNlvAvB20YPvu1K_6UR9CkaPUWjYzT6Jxp9jCY-mUKE-631f6v_cX0DJztkSA</recordid><startdate>20240401</startdate><enddate>20240401</enddate><creator>Tian, Jing</creator><creator>Klavžar, Sandi</creator><creator>Tan, Elif</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-1556-4744</orcidid></search><sort><creationdate>20240401</creationdate><title>Extremal Edge General Position Sets in Some Graphs</title><author>Tian, Jing ; Klavžar, Sandi ; Tan, Elif</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-4809e634422c4402bbb572043f1bd1c98f71a099809cdb1e759c186d1909b143</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Combinatorics</topic><topic>Engineering Design</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Lower bounds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Shortest-path problems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tian, Jing</creatorcontrib><creatorcontrib>Klavžar, Sandi</creatorcontrib><creatorcontrib>Tan, Elif</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tian, Jing</au><au>Klavžar, Sandi</au><au>Tan, Elif</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extremal Edge General Position Sets in Some Graphs</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2024-04-01</date><risdate>2024</risdate><volume>40</volume><issue>2</issue><artnum>40</artnum><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>A set of edges
X
⊆
E
(
G
)
of a graph
G
is an edge general position set if no three edges from
X
lie on a common shortest path. The edge general position number
gp
e
(
G
)
of
G
is the cardinality of a largest edge general position set in
G
. Graphs
G
with
gp
e
(
G
)
=
|
E
(
G
)
|
-
1
and with
gp
e
(
G
)
=
3
are respectively characterized. Sharp upper and lower bounds on
gp
e
(
G
)
are proved for block graphs
G
and exact values are determined for several specific block graphs.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-024-02770-z</doi><orcidid>https://orcid.org/0000-0002-1556-4744</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Graphs and combinatorics, 2024-04, Vol.40 (2), Article 40 |
| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_journals_2987212964 |
| source | SpringerLink Journals |
| subjects | Combinatorics Engineering Design Graph theory Graphs Lower bounds Mathematics Mathematics and Statistics Original Paper Shortest-path problems |
| title | Extremal Edge General Position Sets in Some Graphs |
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