Authors: Luigia Berardi, Mario Gionfriddo, Rosaria Rota
Abstract
An
octagon quadrangle is the graph consisting of an 8-cycle (
x1,...,
x8) with two additional chords: the edges {
x1,
x4} and {
x5,
x8}. An
octagon quadrangle system of order
v and index λ [
OQS] is a pair (
X,
Β), where X is a finite set of
v vertices and
Β is a collection of edge disjoint octagon quadrangles (called
blocks) which partition the edge set of λK
v defined on X. A 4-
kite is the graph having five vertices
x1,
x2,
x3,
x4,
y and consisting of an 4-cycle (
x1,
x2,...,
x4) and an additional edge {
x1,
y}. A 4-
kite design of order
n and index
μ is a pair
K=(
Y,
H), where Y is a finite set of
n vertices and
H is a collection of edge disjoint 4-
kite which partition the edge set of
μKn defined on Y. An
Octagon Kite System [
OKS] of order
v and indices (λ, μ) is an
OQS(
v) of index λ in which it is possible to divide every block in two 4-
kites so that an 4-
kite design of order
v and index μ is defined.
In this paper we determine the spectrum for
OKS(
v) nesting 4-kite-designs of
equi-indices (2,3).
Luigia Berardi Dipartimento di Ingegneria Elettrica e dell'Informazione,
Universitá di L'Aquila
E-mail:
Mario Gionfriddo
Dipartimento di Matematica e Informatica,
Universitá di Catania
E-mail:
Rosaria Rota
Dipartimento di Matematica, Universitá di RomaTre
E-mail:
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