10,055 research outputs found
On global location-domination in graphs
A dominating set of a graph is called locating-dominating, LD-set for
short, if every vertex not in is uniquely determined by the set of
neighbors of belonging to . Locating-dominating sets of minimum
cardinality are called -codes and the cardinality of an LD-code is the
location-domination number . An LD-set of a graph is global
if it is an LD-set of both and its complement . The global
location-domination number is the minimum cardinality of a
global LD-set of . In this work, we give some relations between
locating-dominating sets and the location-domination number in a graph and its
complement.Comment: 15 pages: 2 tables; 8 figures; 20 reference
Extremal Graph Theory for Metric Dimension and Diameter
A set of vertices \emph{resolves} a connected graph if every vertex
is uniquely determined by its vector of distances to the vertices in . The
\emph{metric dimension} of is the minimum cardinality of a resolving set of
. Let be the set of graphs with metric dimension
and diameter . It is well-known that the minimum order of a graph in
is exactly . The first contribution of this
paper is to characterise the graphs in with order
for all values of and . Such a characterisation was
previously only known for or . The second contribution is
to determine the maximum order of a graph in for all
values of and . Only a weak upper bound was previously known
Nordhaus-Gaddum bounds for locating domination
A dominating set S of graph G is called metric-locating-dominating if it is
also locating, that is, if every vertex v is uniquely determined by its vector
of distances to the vertices in S. If moreover, every vertex v not in S is also
uniquely determined by the set of neighbors of v belonging to S, then it is
said to be locating-dominating. Locating, metric-locating-dominating and
locating-dominating sets of minimum cardinality are called b-codes, e-codes and
l-codes, respectively. A Nordhaus-Gaddum bound is a tight lower or upper bound
on the sum or product of a parameter of a graph G and its complement G. In this
paper, we present some Nordhaus-Gaddum bounds for the location number b, the
metric-location-number e and the location-domination number l. Moreover, in
each case, the graph family attaining the corresponding bound is characterized.Comment: 7 pages, 2 figure
Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps
We solve the two-particle s-wave scattering problem for ultracold atom gases
confined in arbitrary quasi-one-dimensional trapping potentials, allowing for
two different atom species. As a consequence, the center-of-mass and relative
degrees of freedom do not factorize. We derive bound-state solutions and obtain
the general scattering solution, which exhibits several resonances in the 1D
scattering length induced by the confinement. We apply our formalism to two
experimentally relevant cases: (i) interspecies scattering in a two-species
mixture, and (ii) the two-body problem for a single species in a non-parabolic
trap.Comment: 22 pages, 3 figure
Expanding Lie (super)algebras through abelian semigroups
We propose an outgrowth of the expansion method introduced by de Azcarraga et
al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the
direct product between an abelian semigroup S and a Lie algebra g. General
conditions under which relevant subalgebras can systematically be extracted
from S \times g are given. We show how, for a particular choice of semigroup S,
the known cases of expanded algebras can be reobtained, while new ones arise
from different choices. Concrete examples, including the M algebra and a
D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit,
non-trace invariant tensors for these S-expanded algebras, which are essential
ingredients in, e.g., the formulation of Supergravity theories in arbitrary
space-time dimensions.Comment: 42 pages, 8 figures. v2: Improved figures, updated notation and
terminolog
L'obra de la Universitat de Cervera, a través dels projectes i les incidències en la construcció
La Universitat de Cervera: anĂ lisi d'un edifici paradigma de l'arquitectura del segle XVIII a Catalunya
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