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Perfect octagon quadrangle systems
An octagon quadrangle is the graph consisting of an 8-cycle ( x 1 , … , x 8 ) with two additional chords: the edges { x 1 , x 4 } and { x 5 , x 8 } . An octagon quadrangle system [ O Q S ] of order v and index λ is a pair ( X , B ) , where X is a finite set of v vertices and B is a collection of edg...
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| Published in: | Discrete mathematics 2010-07, Vol.310 (13), p.1979-1985 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c362t-7d72b6551ef6668ddccc4ace7115dcde82b9e065fb2c9b865dcede3f9b1923393 |
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| cites | cdi_FETCH-LOGICAL-c362t-7d72b6551ef6668ddccc4ace7115dcde82b9e065fb2c9b865dcede3f9b1923393 |
| container_end_page | 1985 |
| container_issue | 13 |
| container_start_page | 1979 |
| container_title | Discrete mathematics |
| container_volume | 310 |
| creator | Berardi, Luigia Gionfriddo, Mario Rota, Rosaria |
| description | An
octagon quadrangle is the graph consisting of an 8-cycle
(
x
1
,
…
,
x
8
)
with two additional chords: the edges
{
x
1
,
x
4
}
and
{
x
5
,
x
8
}
. An
octagon quadrangle system [
O
Q
S
] of order
v
and index
λ
is a pair
(
X
,
B
)
, where
X
is a finite set of
v
vertices and
B
is a collection of edge disjoint octagon quadrangles, which partitions the edge set of
λ
K
v
defined on
X
. An
octagon quadrangle system
Σ
=
(
X
,
B
)
of order
v
and index
λ
is
strongly perfect if the collection of all the
inside 4-cycle and the collection of all the outside 8-cycle quadrangles, contained in the octagon quadrangles, form a
μ
-fold 4-cycle system of order
v
and a
ϱ
-fold 8-cycle system of order
v
, respectively. More generally,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
are also defined. In this paper, following the ideas of
polygon systems introduced by
Lucia Gionfriddo in her papers
[4–7], we determine completely the spectrum of
strongly perfect
O
Q
S
s
,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
, having the minimum possible value for their indices. |
| doi_str_mv | 10.1016/j.disc.2010.03.012 |
| format | article |
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octagon quadrangle is the graph consisting of an 8-cycle
(
x
1
,
…
,
x
8
)
with two additional chords: the edges
{
x
1
,
x
4
}
and
{
x
5
,
x
8
}
. An
octagon quadrangle system [
O
Q
S
] of order
v
and index
λ
is a pair
(
X
,
B
)
, where
X
is a finite set of
v
vertices and
B
is a collection of edge disjoint octagon quadrangles, which partitions the edge set of
λ
K
v
defined on
X
. An
octagon quadrangle system
Σ
=
(
X
,
B
)
of order
v
and index
λ
is
strongly perfect if the collection of all the
inside 4-cycle and the collection of all the outside 8-cycle quadrangles, contained in the octagon quadrangles, form a
μ
-fold 4-cycle system of order
v
and a
ϱ
-fold 8-cycle system of order
v
, respectively. More generally,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
are also defined. In this paper, following the ideas of
polygon systems introduced by
Lucia Gionfriddo in her papers
[4–7], we determine completely the spectrum of
strongly perfect
O
Q
S
s
,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
, having the minimum possible value for their indices.</description><identifier>ISSN: 0012-365X</identifier><identifier>EISSN: 1872-681X</identifier><identifier>DOI: 10.1016/j.disc.2010.03.012</identifier><identifier>CODEN: DSMHA4</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Algebra ; Applied sciences ; Collection ; Combinatorics ; Combinatorics. Ordered structures ; Computer science; control theory; systems ; Designs and configurations ; Exact sciences and technology ; G-designs ; Geometry ; Graphs ; Information retrieval. Graph ; Mathematical analysis ; Mathematics ; Partitions ; Polygon systems ; Polygons ; Sciences and techniques of general use ; Theoretical computing</subject><ispartof>Discrete mathematics, 2010-07, Vol.310 (13), p.1979-1985</ispartof><rights>2010 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c362t-7d72b6551ef6668ddccc4ace7115dcde82b9e065fb2c9b865dcede3f9b1923393</citedby><cites>FETCH-LOGICAL-c362t-7d72b6551ef6668ddccc4ace7115dcde82b9e065fb2c9b865dcede3f9b1923393</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,783,787,27936,27937</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22757820$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Berardi, Luigia</creatorcontrib><creatorcontrib>Gionfriddo, Mario</creatorcontrib><creatorcontrib>Rota, Rosaria</creatorcontrib><title>Perfect octagon quadrangle systems</title><title>Discrete mathematics</title><description>An
octagon quadrangle is the graph consisting of an 8-cycle
(
x
1
,
…
,
x
8
)
with two additional chords: the edges
{
x
1
,
x
4
}
and
{
x
5
,
x
8
}
. An
octagon quadrangle system [
O
Q
S
] of order
v
and index
λ
is a pair
(
X
,
B
)
, where
X
is a finite set of
v
vertices and
B
is a collection of edge disjoint octagon quadrangles, which partitions the edge set of
λ
K
v
defined on
X
. An
octagon quadrangle system
Σ
=
(
X
,
B
)
of order
v
and index
λ
is
strongly perfect if the collection of all the
inside 4-cycle and the collection of all the outside 8-cycle quadrangles, contained in the octagon quadrangles, form a
μ
-fold 4-cycle system of order
v
and a
ϱ
-fold 8-cycle system of order
v
, respectively. More generally,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
are also defined. In this paper, following the ideas of
polygon systems introduced by
Lucia Gionfriddo in her papers
[4–7], we determine completely the spectrum of
strongly perfect
O
Q
S
s
,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
, having the minimum possible value for their indices.</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>Collection</subject><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Computer science; control theory; systems</subject><subject>Designs and configurations</subject><subject>Exact sciences and technology</subject><subject>G-designs</subject><subject>Geometry</subject><subject>Graphs</subject><subject>Information retrieval. Graph</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Partitions</subject><subject>Polygon systems</subject><subject>Polygons</subject><subject>Sciences and techniques of general use</subject><subject>Theoretical computing</subject><issn>0012-365X</issn><issn>1872-681X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LAzEUDKJgrf4BT0UQT7vmo_lY8CLFLyjoQaG3kE1eSsp2t022Qv-9WVs8enq8YWbem0HomuCSYCLuV6ULyZYUZwCzEhN6gkZESVoIRRanaIQzVDDBF-foIqUVzrtgaoRuPiB6sP2ks71Zdu1kuzMumnbZwCTtUw_rdInOvGkSXB3nGH09P33OXov5-8vb7HFeWCZoX0gnaS04J-CFEMo5a-3UWJCEcGcdKFpXgAX3NbVVrUQGwQHzVU0qyljFxuju4LuJ3XYHqdfrnAmaxrTQ7ZKWnIkpp79MemDa2KUUwetNDGsT95pgPfShV3roQw99aMx0Dp9Ft0d7k6xpfA5pQ_pTUiq5VBRn3sOBBznrd4Cokw3Q5mdDzEVp14X_zvwA60x17A</recordid><startdate>20100728</startdate><enddate>20100728</enddate><creator>Berardi, Luigia</creator><creator>Gionfriddo, Mario</creator><creator>Rota, Rosaria</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><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></search><sort><creationdate>20100728</creationdate><title>Perfect octagon quadrangle systems</title><author>Berardi, Luigia ; Gionfriddo, Mario ; Rota, Rosaria</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-7d72b6551ef6668ddccc4ace7115dcde82b9e065fb2c9b865dcede3f9b1923393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Applied sciences</topic><topic>Collection</topic><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Computer science; control theory; systems</topic><topic>Designs and configurations</topic><topic>Exact sciences and technology</topic><topic>G-designs</topic><topic>Geometry</topic><topic>Graphs</topic><topic>Information retrieval. Graph</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Partitions</topic><topic>Polygon systems</topic><topic>Polygons</topic><topic>Sciences and techniques of general use</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Berardi, Luigia</creatorcontrib><creatorcontrib>Gionfriddo, Mario</creatorcontrib><creatorcontrib>Rota, Rosaria</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><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 mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Berardi, Luigia</au><au>Gionfriddo, Mario</au><au>Rota, Rosaria</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Perfect octagon quadrangle systems</atitle><jtitle>Discrete mathematics</jtitle><date>2010-07-28</date><risdate>2010</risdate><volume>310</volume><issue>13</issue><spage>1979</spage><epage>1985</epage><pages>1979-1985</pages><issn>0012-365X</issn><eissn>1872-681X</eissn><coden>DSMHA4</coden><abstract>An
octagon quadrangle is the graph consisting of an 8-cycle
(
x
1
,
…
,
x
8
)
with two additional chords: the edges
{
x
1
,
x
4
}
and
{
x
5
,
x
8
}
. An
octagon quadrangle system [
O
Q
S
] of order
v
and index
λ
is a pair
(
X
,
B
)
, where
X
is a finite set of
v
vertices and
B
is a collection of edge disjoint octagon quadrangles, which partitions the edge set of
λ
K
v
defined on
X
. An
octagon quadrangle system
Σ
=
(
X
,
B
)
of order
v
and index
λ
is
strongly perfect if the collection of all the
inside 4-cycle and the collection of all the outside 8-cycle quadrangles, contained in the octagon quadrangles, form a
μ
-fold 4-cycle system of order
v
and a
ϱ
-fold 8-cycle system of order
v
, respectively. More generally,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
are also defined. In this paper, following the ideas of
polygon systems introduced by
Lucia Gionfriddo in her papers
[4–7], we determine completely the spectrum of
strongly perfect
O
Q
S
s
,
C
4
-perfect
O
Q
S
s
and
C
8
-perfect
O
Q
S
s
, having the minimum possible value for their indices.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.disc.2010.03.012</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-365X |
| ispartof | Discrete mathematics, 2010-07, Vol.310 (13), p.1979-1985 |
| issn | 0012-365X 1872-681X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_753645239 |
| source | ScienceDirect Freedom Collection |
| subjects | Algebra Applied sciences Collection Combinatorics Combinatorics. Ordered structures Computer science control theory systems Designs and configurations Exact sciences and technology G-designs Geometry Graphs Information retrieval. Graph Mathematical analysis Mathematics Partitions Polygon systems Polygons Sciences and techniques of general use Theoretical computing |
| title | Perfect octagon quadrangle systems |
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