10.1 Graphs and Graph Models

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Presentation transcript:

10.1 Graphs and Graph Models Dr. Halimah Alshehri

Graphs DEFINITION 1 A graph G = ( V , E) consists of V, a nonempty set of vertices (or nodes) and E, a set of edges. Each edge has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints. A graph with an infinite vertex set or an infinite number of edges is called an infinite graph. a graph with a finite vertex set and a finite edge set is called a finite graph. Dr. Halimah Alshehri

The Types of Graphs Simple graph: A graph in which each edge connects two different vertices and where no two edges connect the same pair of vertices. Dr. Halimah Alshehri

Loop is a closed curve whose initial and final vertices coincide. Multigraphs: Graphs that may have multiple edges connecting the same vertices. Loop is a closed curve whose initial and final vertices coincide. Dr. Halimah Alshehri

Pseudographs : Graphs that may include loops, (and possibly multiple edges connecting the same pair of vertices). Dr. Halimah Alshehri

Directed & Undirected Graphs Definition2 A directed graph (or digraph) ( V,E) consists of a nonempty set of vertices V and a set of directed edges (or arcs) E. Each directed edge is associated with an ordered pair of vertices. The directed edge associated with the ordered pair (u ,v) is said to start at u and end at v. undirected graphs. Their edges are also said to be undirected. Dr. Halimah Alshehri

Types of Directed & Undirected Graphs simple directed graph a directed graph that has no loops and has no multiple directed edges. Directed multigraphs: directed graphs that may have multiple directed edges. Edge of multiplicity m When there are m directed edges, each associated to an ordered pair of vertices (u,v). Dr. Halimah Alshehri

Mixed graph: a graph with both directed and undirected edges. Dr. Halimah Alshehri

Homework Page 650 3 4 5 7 9 Dr. Halimah Alshehri