7,582 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
Moduli spaces of toric manifolds
We construct a distance on the moduli space of symplectic toric manifolds of
dimension four. Then we study some basic topological properties of this space,
in particular, path-connectedness, compactness, and completeness. The
construction of the distance is related to the Duistermaat-Heckman measure and
the Hausdorff metric. While the moduli space, its topology and metric, may be
constructed in any dimension, the tools we use in the proofs are
four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version,
19 pages, 6 figure
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