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Groupoid C*-algebras with Hausdorff Spectrum
Groupoid C*-algebras with Hausdorff Spectrum

... Suppose that the maps of H/Hx onto H · x are homeomorphisms for each x ∈ X . The spectrum C ∗ (H n X )∧ is Hausdorff if and only if the map x 7→ Hx is continuous with respect to the Fell topology and X /H is Hausdorff. Note: We can use [Orloff Clark; 07] and [Ramsay; 90] to show that if either X /H ...
arXiv:1510.01797v3 [math.CT] 21 Apr 2016 - Mathematik, Uni
arXiv:1510.01797v3 [math.CT] 21 Apr 2016 - Mathematik, Uni

The Min-Max Voronoi Diagram of Polygons and Applications in VLSI
The Min-Max Voronoi Diagram of Polygons and Applications in VLSI

Congruence graphs and newforms
Congruence graphs and newforms

A proof of the Kepler conjecture
A proof of the Kepler conjecture

The geometry of orthogonal groups over finite fields
The geometry of orthogonal groups over finite fields

Incidence structures I. Constructions of some famous combinatorial
Incidence structures I. Constructions of some famous combinatorial

[edit] Star polyhedra
[edit] Star polyhedra

... dimensionality of -1. These posets belong to the larger family of abstract polytopes in any number of dimensions. ...
on three classes of regular toroids
on three classes of regular toroids

pg 349 #1-16 all, 47, 48, 49
pg 349 #1-16 all, 47, 48, 49

On the Domination and Total Domination Numbers of Cayley Sum
On the Domination and Total Domination Numbers of Cayley Sum

Ranking Arguments With Compensation
Ranking Arguments With Compensation

Edge Detour Monophonic Number of a Graph
Edge Detour Monophonic Number of a Graph

3-3 Solving Inequalities by Multiplying or Dividing
3-3 Solving Inequalities by Multiplying or Dividing

MATHEMATICS MAGAZINE
MATHEMATICS MAGAZINE

... posed questions as to which collections of animals can be transformed by Mad Vet machines into other collections. Recently, such scenarios have been used as the basis of various problem solving and Math Circle activities; see, for instance, [13]. In this article we take a different approach, using M ...
Arrangements and duality
Arrangements and duality

State whether each sentence is true or false . If false , replace the
State whether each sentence is true or false . If false , replace the

D--MAHESH-NEWWAV~3-Chapter 40004.mdi
D--MAHESH-NEWWAV~3-Chapter 40004.mdi

Minimal tangent visibility graphs
Minimal tangent visibility graphs

Spherical Geometry Toolkit Documentation
Spherical Geometry Toolkit Documentation

Topic 3 Space, Shape and Orientation
Topic 3 Space, Shape and Orientation

...  If two triangles are equiangular, their corresponding sides are in proportion.  If two triangles have their corresponding sides in proportion, they are equiangular.  'Equiangular' means 'equal angles' which means that the three angles of the one triangle are equal in size to the three angles of ...
Parabolas
Parabolas

... We saw in Section 3.1 that the graph of the equation y = ax2 + bx + c is a U-shaped curve called a parabola that opens either upward or downward—depending on whether the sign of a is positive or negative. • Here, we study parabolas from a geometric rather than an algebraic point of view. ...
DuarteFrancisSeville30apr13
DuarteFrancisSeville30apr13

... The fundamental fact that, in the plane, any 4-sided polygon with equal length sides must be a rhombus, leads us to consider rhombic frameworks in general. Endowed with the additional topological properties, we call them rhombic carpets. In particular, when the rhombi are squares, we shall call them ...
Hankel Matrices: From Words to Graphs
Hankel Matrices: From Words to Graphs

Stability of Quasicrystal Frameworks in 2D and 3D
Stability of Quasicrystal Frameworks in 2D and 3D

1 2 3 4 5 ... 25 >

Dual graph



In the mathematical discipline of graph theory, the dual graph of a plane graph G is a graph that has a vertex for each face of G. The dual graph has an edge whenever two faces of G are separated from each other by an edge. Thus, each edge e of G has a corresponding dual edge, the edge that connects the two faces on either side of e.Graph duality is a topological generalization of the geometric concepts of dual polyhedra and dual tessellations, and is in turn generalized algebraically by the concept of a dual matroid. Variations of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded onto non-planar two-dimensional surfaces.However, the notion described in this page is different from the edge-to-vertex dual (line graph) of a graph and should not be confused with it.The term ""dual"" is used because this property is symmetric, meaning that if H is a dual of G, then G is a dual of H (if G is connected). When discussing the dual of a graph G, the graph G itself may be referred to as the ""primal graph"". Many other graph properties and structures may be translated into other natural properties and structures of the dual. For instance, cycles are dual to cuts, spanning trees are dual to the complements of spanning trees, and simple graphs (without parallel edges or self-loops) are dual to 3-edge-connected graphs.Polyhedral graphs, and some other planar graphs, have unique dual graphs. However, for planar graphs more generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph. Testing whether one planar graph is dual to another is NP-complete.
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