A family of symmetric graphs in relation to 2-point-transitive linear spaces
A graph Γ is G -symmetric if it admits G as a group of automorphisms acting transitively on the set of arcs of Γ , where an arc is an ordered pair of adjacent vertices. Let Γ be a G -symmetric graph such that its vertex set admits a nontrivial G -invariant partition B , and let D ( Γ , B ) be the in...
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| Veröffentlicht in: | Journal of algebraic combinatorics 2025-02, Vol.61 (1), Article 7 |
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| creator | Fang, Teng Zhou, Sanming Zhou, Shenglin |
| description | A graph
Γ
is
G
-symmetric if it admits
G
as a group of automorphisms acting transitively on the set of arcs of
Γ
, where an arc is an ordered pair of adjacent vertices. Let
Γ
be a
G
-symmetric graph such that its vertex set admits a nontrivial
G
-invariant partition
B
, and let
D
(
Γ
,
B
)
be the incidence structure with point set
B
and blocks
{
B
}
∪
Γ
B
(
α
)
, for
B
∈
B
and
α
∈
B
, where
Γ
B
(
α
)
is the set of blocks of
B
containing at least one neighbor of
α
in
Γ
. In this paper, we classify all
G
-symmetric graphs
Γ
such that
Γ
B
(
α
)
≠
Γ
B
(
β
)
for distinct
α
,
β
∈
B
, the quotient graph of
Γ
with respect to
B
is a complete graph, and
D
(
Γ
,
B
)
is isomorphic to the complement of a (
G
, 2)-point-transitive linear space. |
| doi_str_mv | 10.1007/s10801-024-01368-1 |
| format | Article |
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Γ
is
G
-symmetric if it admits
G
as a group of automorphisms acting transitively on the set of arcs of
Γ
, where an arc is an ordered pair of adjacent vertices. Let
Γ
be a
G
-symmetric graph such that its vertex set admits a nontrivial
G
-invariant partition
B
, and let
D
(
Γ
,
B
)
be the incidence structure with point set
B
and blocks
{
B
}
∪
Γ
B
(
α
)
, for
B
∈
B
and
α
∈
B
, where
Γ
B
(
α
)
is the set of blocks of
B
containing at least one neighbor of
α
in
Γ
. In this paper, we classify all
G
-symmetric graphs
Γ
such that
Γ
B
(
α
)
≠
Γ
B
(
β
)
for distinct
α
,
β
∈
B
, the quotient graph of
Γ
with respect to
B
is a complete graph, and
D
(
Γ
,
B
)
is isomorphic to the complement of a (
G
, 2)-point-transitive linear space.</description><identifier>ISSN: 0925-9899</identifier><identifier>EISSN: 1572-9192</identifier><identifier>DOI: 10.1007/s10801-024-01368-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Apexes ; Automorphisms ; Combinatorics ; Computer Science ; Convex and Discrete Geometry ; Graph theory ; Graphs ; Group Theory and Generalizations ; Lattices ; Mathematics ; Mathematics and Statistics ; Order ; Ordered Algebraic Structures ; Vector spaces ; Vertex sets</subject><ispartof>Journal of algebraic combinatorics, 2025-02, Vol.61 (1), Article 7</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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-c200t-7ffc9401ad40570d6c23745771534c0d9f703c364d90a1cad999f89bf80f51c43</cites><orcidid>0000-0001-9854-6076</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/s10801-024-01368-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10801-024-01368-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Fang, Teng</creatorcontrib><creatorcontrib>Zhou, Sanming</creatorcontrib><creatorcontrib>Zhou, Shenglin</creatorcontrib><title>A family of symmetric graphs in relation to 2-point-transitive linear spaces</title><title>Journal of algebraic combinatorics</title><addtitle>J Algebr Comb</addtitle><description>A graph
Γ
is
G
-symmetric if it admits
G
as a group of automorphisms acting transitively on the set of arcs of
Γ
, where an arc is an ordered pair of adjacent vertices. Let
Γ
be a
G
-symmetric graph such that its vertex set admits a nontrivial
G
-invariant partition
B
, and let
D
(
Γ
,
B
)
be the incidence structure with point set
B
and blocks
{
B
}
∪
Γ
B
(
α
)
, for
B
∈
B
and
α
∈
B
, where
Γ
B
(
α
)
is the set of blocks of
B
containing at least one neighbor of
α
in
Γ
. In this paper, we classify all
G
-symmetric graphs
Γ
such that
Γ
B
(
α
)
≠
Γ
B
(
β
)
for distinct
α
,
β
∈
B
, the quotient graph of
Γ
with respect to
B
is a complete graph, and
D
(
Γ
,
B
)
is isomorphic to the complement of a (
G
, 2)-point-transitive linear space.</description><subject>Apexes</subject><subject>Automorphisms</subject><subject>Combinatorics</subject><subject>Computer Science</subject><subject>Convex and Discrete Geometry</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Group Theory and Generalizations</subject><subject>Lattices</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Order</subject><subject>Ordered Algebraic Structures</subject><subject>Vector spaces</subject><subject>Vertex sets</subject><issn>0925-9899</issn><issn>1572-9192</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEURoMoWKt_wFXAdfTeZDKZLEvxBQU3ug4xk9SUeZlEof_e0QruXN3NOd-FQ8glwjUCqJuM0AAy4BUDFHXD8IgsUCrONGp-TBaguWS60fqUnOW8AwDdoFyQzYoG28duT8dA877vfUnR0W2y01umcaDJd7bEcaBlpJxNYxwKK8kOOZb46WkXB28TzZN1Pp-Tk2C77C9-75K83N0-rx_Y5un-cb3aMMcBClMhOF0B2rYCqaCtHReqkkqhFJWDVgcFwom6ajVYdLbVWodGv4YGgkRXiSW5OuxOaXz_8LmY3fiRhvmlESgqwWtUcqb4gXJpzDn5YKYUe5v2BsF8VzOHamauZn6qGZwlcZDyDA9bn_6m_7G-AExkbp8</recordid><startdate>20250201</startdate><enddate>20250201</enddate><creator>Fang, Teng</creator><creator>Zhou, Sanming</creator><creator>Zhou, Shenglin</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9854-6076</orcidid></search><sort><creationdate>20250201</creationdate><title>A family of symmetric graphs in relation to 2-point-transitive linear spaces</title><author>Fang, Teng ; Zhou, Sanming ; Zhou, Shenglin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-7ffc9401ad40570d6c23745771534c0d9f703c364d90a1cad999f89bf80f51c43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>Apexes</topic><topic>Automorphisms</topic><topic>Combinatorics</topic><topic>Computer Science</topic><topic>Convex and Discrete Geometry</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Group Theory and Generalizations</topic><topic>Lattices</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Order</topic><topic>Ordered Algebraic Structures</topic><topic>Vector spaces</topic><topic>Vertex sets</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fang, Teng</creatorcontrib><creatorcontrib>Zhou, Sanming</creatorcontrib><creatorcontrib>Zhou, Shenglin</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of algebraic combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fang, Teng</au><au>Zhou, Sanming</au><au>Zhou, Shenglin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A family of symmetric graphs in relation to 2-point-transitive linear spaces</atitle><jtitle>Journal of algebraic combinatorics</jtitle><stitle>J Algebr Comb</stitle><date>2025-02-01</date><risdate>2025</risdate><volume>61</volume><issue>1</issue><artnum>7</artnum><issn>0925-9899</issn><eissn>1572-9192</eissn><abstract>A graph
Γ
is
G
-symmetric if it admits
G
as a group of automorphisms acting transitively on the set of arcs of
Γ
, where an arc is an ordered pair of adjacent vertices. Let
Γ
be a
G
-symmetric graph such that its vertex set admits a nontrivial
G
-invariant partition
B
, and let
D
(
Γ
,
B
)
be the incidence structure with point set
B
and blocks
{
B
}
∪
Γ
B
(
α
)
, for
B
∈
B
and
α
∈
B
, where
Γ
B
(
α
)
is the set of blocks of
B
containing at least one neighbor of
α
in
Γ
. In this paper, we classify all
G
-symmetric graphs
Γ
such that
Γ
B
(
α
)
≠
Γ
B
(
β
)
for distinct
α
,
β
∈
B
, the quotient graph of
Γ
with respect to
B
is a complete graph, and
D
(
Γ
,
B
)
is isomorphic to the complement of a (
G
, 2)-point-transitive linear space.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10801-024-01368-1</doi><orcidid>https://orcid.org/0000-0001-9854-6076</orcidid></addata></record> |
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| ispartof | Journal of algebraic combinatorics, 2025-02, Vol.61 (1), Article 7 |
| issn | 0925-9899 1572-9192 |
| language | eng |
| recordid | cdi_proquest_journals_3134326175 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Apexes Automorphisms Combinatorics Computer Science Convex and Discrete Geometry Graph theory Graphs Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Vector spaces Vertex sets |
| title | A family of symmetric graphs in relation to 2-point-transitive linear spaces |
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