Introduction to Graphs

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Graphs and Trees

Graphs and Trees. This handout: Application examples. Athens area map. Telephone network. Molecular chain of atoms in protein. Graphs in our daily lives. Transportation Telephone Computer Electrical (power) Pipelines Molecular structures in biochemistry.

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Graphs, Networks, Trees

Graphs, Networks, Trees. Examples for in class. Visual Web Website as graphs (http:// www.aharef.info/2006/05/websites_as_graphs.htm) Dr H’s SILS Try one.. Touchgraph Amazon>Movies “Redford”, “Streep” Try one… Viszter. Graphs, Networks, Trees.

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Introduction to Graphs

Introduction to Graphs. Introduction. Graphs are a generalization of trees Nodes or verticies Edges or arcs Two kinds of graphs Directed Undirected. Introduction: Formal Definition. A graph G = (V,E) consists of a finite set of vertices, V, and a finite set of edges E.

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Introduction to Trees

Introduction to Trees. Joe Meehean. Conceptual Picture. A. B. I. C. D. E. X. Conceptual Picture. A. B. I. C. D. E. X. Terminology e ach circle is a node pointers are edges t opmost node is the root b ottom nodes are leaves no outgoing edges Every non-empty tree has

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MAFSM: From Trees to Graphs

MAFSM: From Trees to Graphs. e. B n. B B. B A. B B B B. B A B A. B A B B. B B B A. . . . . . . . . . . . . MAFSM: From Trees to Graphs. e. B n. B B. B A. B B B B. B A B A. B A B B. B B B A. . . . . . Front ( B n ). . . . . . . .

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Graphs and Trees

Graphs and Trees. This handout: Eulerian Cycles: Sufficiency of the condition Hamiltonian tour. 4. 7. 3. 5. More on Euler’s Theorem.

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Graphs and Trees

Graphs and Trees. This handout: Total degree of a graph Applications of Graphs. Graph properties. Definition : The total degree of a graph is the sum of the degrees of all its nodes. Theorem: If G is any graph, then the total degree of G equals twice the number of edges of G :

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Graphs and Trees

Graphs and Trees. This handout: Terminology of Graphs Applications of Graphs. Derive properties, get applications. Using the tools of logical reasoning. Mathematical objects. numbers. sets. functions. graphs. The process of mathematical reasoning.

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Introduction to Graphs

Introduction to Graphs. Lecture 7: Sep 24. (based on slides in MIT 6.042). Seven Bridges of Königsberg. Is it possible to walk with a route that crosses each bridge exactly once?. Seven Bridges of Königsberg. Forget even more. Forget unimportant details. A Graph. An edge (or a line).

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Introduction to Trees

Introduction to Trees. when here. we can only go here. if here. then here. or here. Tree. Graph. Trees. Motivation. When at a node in a singly linked list, there is no choice as to which node can be visited next:.

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Introduction to Graphs

Introduction to Graphs. Lecture 18: Nov 16. Seven Bridges of Königsberg. Is it possible to walk with a route that crosses each bridge exactly once?. Seven Bridges of Königsberg. Forget even more. Forget unimportant details. A Graph. An edge (or a line). A vertex (or a node,

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Graphs and Trees

Graphs and Trees. More examples on Total degree of a graph Applications of Graphs. Handshakes at a party.

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Introduction to Graphs

Introduction to Graphs. Graphs: what are they?. Representations of pairwise relationships Collections of objects under some specified relationship. Graphs: what are they mathematically?. A graph G is a pair (V,E) V is a set of vertices (nodes) E is a set of pairs ( a,b ), a,b  V

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Introduction to Graphs

Introduction to Graphs. Graph Definition. Graph : consists of vertices and edges. Each edge must start and end at a vertex. Graph G = ( V , E ) V = set of vertices E = set of edges  ( V  V ) Example:. www.cs.unc.edu/~plaisted/comp122/19-graph1.ppt. Graph Definition.

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Introduction to Trees

Introduction to Trees. when here. we can only go here. if here. then here. or here. Tree. Graph. Trees. Motivation. When at a node in a singly linked list, there is no choice as to which node can be visited next:.

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Graphs and Trees

Graphs and Trees. This handout: Trees Minimum Spanning Tree Problem www.ohio.edu/people/melkonia/math3050/.../ trees . ppt. Terminology of Graphs: Cycles, Connectivity and Trees. A path that begins and ends at the same node is called a cycle . Example:

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Graphs and Trees

Graphs and Trees. More examples on Total degree of a graph Applications of Graphs. Handshakes at a party.

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Introduction to Graphs

Campus map Travelling salesperson Circuit layout. Project scheduling Oil flow Flight scheduling. Introduction to Graphs.

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Graphs and Trees

Graphs and Trees. This handout: Total degree of a graph Applications of Graphs. Graph properties. Definition : The total degree of a graph is the sum of the degrees of all its nodes. Theorem: If G is any graph, then the total degree of G equals twice the number of edges of G :

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