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Distinguishing geometric graphs
Journal of Graph Theory, 2006AbstractWe begin the study of distinguishing geometric graphs. Let G be a geometric graph. An automorphism of the underlying graph that preserves both crossings and noncrossings is called a geometric automorphism. A labeling, f: V(G) → {1, 2, … , r}, is said to be r‐distinguishing if no nontrivial geometric automorphism preserves the labels.
Michael O. Albertson, Debra L. Boutin
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Journal of Graph Theory, 2011
AbstractA geometric graph is a simple graph drawn on points in the plane, in general position, with straightline edges. A geometric homomorphism from to is a vertex map that preserves adjacencies and crossings. This work proves some basic properties of geometric homomorphisms and defines the geochromatic number as the minimum n so that there is a ...
Debra L. Boutin, Sally Cockburn
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AbstractA geometric graph is a simple graph drawn on points in the plane, in general position, with straightline edges. A geometric homomorphism from to is a vertex map that preserves adjacencies and crossings. This work proves some basic properties of geometric homomorphisms and defines the geochromatic number as the minimum n so that there is a ...
Debra L. Boutin, Sally Cockburn
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1975
The properties of a finite graph (only type considered) may be divided into two distinct groups: geometric, really topological properties, and algebraic properties. In the present chapter, we present the geometry of a graph and in the next its algebra.
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The properties of a finite graph (only type considered) may be divided into two distinct groups: geometric, really topological properties, and algebraic properties. In the present chapter, we present the geometry of a graph and in the next its algebra.
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2017
In this chapter, we discuss the random geometric graph (also called the unit disk graph ) which is an important model for spatial networks. We will also introduce and discuss some of the variants of this model. The random geometric graph is obtained from a random distribution of points in the plane and a geometric rule for connecting these points and ...
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In this chapter, we discuss the random geometric graph (also called the unit disk graph ) which is an important model for spatial networks. We will also introduce and discuss some of the variants of this model. The random geometric graph is obtained from a random distribution of points in the plane and a geometric rule for connecting these points and ...
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Distinct Classes of Complex Structural Variation Uncovered across Thousands of Cancer Genome Graphs
Cell, 2020Kevin Hadi +2 more
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