National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of...

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Transcript of National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of...

Page 1: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 2: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 3: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 4: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 5: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 6: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 7: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 8: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 9: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices
Page 10: National University of Singaporecs5234/2003/spanningtrees.pdf · 2003-08-22 · 2. The space of plane spanning trees on a Euclidean graph Consider a graph G (V, E, w) with n vertices

Graph & BFS. Graph & BFS / Slide 2 Graphs * Extremely useful tool in modeling problems * Consist of: n Vertices n Edges D E A C F B Vertex Edge Vertices.

Graph & BFS. Graph & BFS / Slide 2 Graphs * Extremely useful tool in modeling problems * Consist of: n Vertices n Edges D E A C F B Vertex Edge Vertices.

Graph Algorithms. Representations of graphs ： undirected graph An undirected graph G have five vertices and seven edges An adjacency-list representation.

Graph Algorithms. Representations of graphs ： undirected graph An undirected graph G have five vertices and seven edges An adjacency-list representation.

Ramsey Theory - Mathematicsmath.mit.edu/.../3-ChandlerRamseyTheoryTalk.pdf · 2014-01-08 · Complete Graph K n K n is a complete graph with n vertices if each pair of vertices in

Ramsey Theory - Mathematicsmath.mit.edu/.../3-ChandlerRamseyTheoryTalk.pdf · 2014-01-08 · Complete Graph K n K n is a complete graph with n vertices if each pair of vertices in

Graph Algorithms Searching. Review: Graphs ● A graph G = (V, E) ■ V = set of vertices, E = set of edges ■ Dense graph: |E| |V| 2 ; Sparse graph: |E|

Graph Algorithms Searching. Review: Graphs ● A graph G = (V, E) ■ V = set of vertices, E = set of edges ■ Dense graph: |E| |V| 2 ; Sparse graph: |E|

Elementary Graph Algorithms CLRS Chapter 22. Graph A graph is a structure that consists of a set of vertices and a set of edges between pairs of vertices.

Elementary Graph Algorithms CLRS Chapter 22. Graph A graph is a structure that consists of a set of vertices and a set of edges between pairs of vertices.

Jonathan L. Gross- Genus distribution of graph amalgamations: self-pasting at root-vertices

Jonathan L. Gross- Genus distribution of graph amalgamations: self-pasting at root-vertices

EXAMPLE 1 Graph an equation of an ellipse Graph the equation 4x 2 + 25y 2 = 100. Identify the vertices, co-vertices, and foci of the ellipse. SOLUTION.

EXAMPLE 1 Graph an equation of an ellipse Graph the equation 4x 2 + 25y 2 = 100. Identify the vertices, co-vertices, and foci of the ellipse. SOLUTION.

Chapter 14 Aimee's Work 2003 Instructor's Edition · CHAPTER FOURTEEN GRAPH THEORY Exercise Set 14.1 1. A graph is a finite set of points, called vertices, that are connected with

Chapter 14 Aimee's Work 2003 Instructor's Edition · CHAPTER FOURTEEN GRAPH THEORY Exercise Set 14.1 1. A graph is a finite set of points, called vertices, that are connected with

Basic Graph Terminology A graph consists of a nonempty set of points or vertices, and a set of edges that link together the vertices. A simple real world.

Basic Graph Terminology A graph consists of a nonempty set of points or vertices, and a set of edges that link together the vertices. A simple real world.

Graph Theory Arnold Mesa. Basic Concepts n A graph G = (V,E) is defined by a set of vertices and edges v3 v1 v2Vertex (v1) Edge (e1) A Graph with 3 vertices.

Graph Theory Arnold Mesa. Basic Concepts n A graph G = (V,E) is defined by a set of vertices and edges v3 v1 v2Vertex (v1) Edge (e1) A Graph with 3 vertices.

ETERNAL DOMINATION Chip Klostermeyer. Graph 6 vertices 7 edges Dominating Set γ=2.

ETERNAL DOMINATION Chip Klostermeyer. Graph 6 vertices 7 edges Dominating Set γ=2.

Graph Theoretic Concepts. What is a graph? A set of vertices (or nodes) linked by edges Mathematically, we often write G = (V,E) V: set of vertices,

Graph Theoretic Concepts. What is a graph? A set of vertices (or nodes) linked by edges Mathematically, we often write G = (V,E) V: set of vertices,

Lecture 11 Graph Algorithms. Definitions Graph is a set of vertices V, with edges connecting some of the vertices (edge set E). An edge can connect two.

Lecture 11 Graph Algorithms. Definitions Graph is a set of vertices V, with edges connecting some of the vertices (edge set E). An edge can connect two.

Graph Partitioning Abhiram Ranade IIT Bombay. A load balancing problem Input: – undirected graph G. Vertices = processes. Edges = interprocess communication.

Graph Partitioning Abhiram Ranade IIT Bombay. A load balancing problem Input: – undirected graph G. Vertices = processes. Edges = interprocess communication.

Graph Coloring - UTKweb.eecs.utk.edu/.../coloring_pres.pdfSudoku can be represented as a graph coloring problem Transform the board into a graph with 81 vertices where two vertices

Graph Coloring - UTKweb.eecs.utk.edu/.../coloring_pres.pdfSudoku can be represented as a graph coloring problem Transform the board into a graph with 81 vertices where two vertices

nvGRAPH Library User's Guide - Nvidia · the graph object, called the "graph descriptor", which represents the graph topology and its data. Graph data can be attached to vertices

nvGRAPH Library User's Guide - Nvidia · the graph object, called the "graph descriptor", which represents the graph topology and its data. Graph data can be attached to vertices

Handling limits of high degree vertices in graph …...Handling limits of high degree vertices in graph processing using MapReduce and Pregel M. Al Hajj Hassan1 and Mostafa Bamha2

Handling limits of high degree vertices in graph …...Handling limits of high degree vertices in graph processing using MapReduce and Pregel M. Al Hajj Hassan1 and Mostafa Bamha2

Graph-based Clusteringcse.msu.edu/~cse802/S17/slides/Lec_20_21_22_Clustering.pdf · Graph-based Clustering Transform the data into a graph representation –Vertices are the data

Graph-based Clusteringcse.msu.edu/~cse802/S17/slides/Lec_20_21_22_Clustering.pdf · Graph-based Clustering Transform the data into a graph representation –Vertices are the data

Graph Coloring - UTKweb.eecs.utk.edu/.../coloring_pres.pdf · Vertex Coloring Proper vertex coloring - Labeling of all vertices in a graph such that no two vertices sharing an edge

Graph Coloring - UTKweb.eecs.utk.edu/.../coloring_pres.pdf · Vertex Coloring Proper vertex coloring - Labeling of all vertices in a graph such that no two vertices sharing an edge

Graph-based Segmentation. Main Ideas Convert image into a graph Vertices for the pixels Vertices for the pixels Edges between the pixels Edges between.

Graph-based Segmentation. Main Ideas Convert image into a graph Vertices for the pixels Vertices for the pixels Edges between the pixels Edges between.