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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 |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | 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. |
|---|---|
| ISSN: | 0012-365X 1872-681X |
| DOI: | 10.1016/j.disc.2010.03.012 |