Download presentation

Presentation is loading. Please wait.

Published bySkyler Flemmings Modified over 3 years ago

1
Discrete Mathematics University of Jazeera College of Information Technology & Design Khulood Ghazal Connectivity Lecture _13

2
Paths in Undirected Graphs There is a path from vertex v 0 to vertex v n if there is a sequence of edges from v 0 to v n –This path is labeled as v 0,v 1,v 2,…,v n and has a length of n. The path is a circuit if the path begins and ends with the same vertex. A path is simple if it does not contain the same edge more than once.

3
Paths in Undirected Graphs A path or circuit is said to pass through the vertices v 0, v 1, v 2, …, v n or traverse the edges e 1, e 2, …, e n.

4
Example u 1, u 4, u 2, u 3 –Is it simple? –yes –What is the length? –3 –Does it have any circuits? –no u 1 u 2 u 5 u 4 u 3

5
Example u 1, u 5, u 4, u 1, u 2, u 3 –Is it simple? –yes –What is the length? –5 –Does it have any circuits? –Yes; u 1, u 5, u 4, u 1 u 1 u 2 u 5 u 3 u 4

6
Example u 1, u 2, u 5, u 4, u 3 –Is it simple? –yes –What is the length? –4 –Does it have any circuits? –no u 1 u 2 u 5 u 3 u 4

7
Connectedness An undirected graph is called connected if there is a path between every pair of distinct vertices of the graph. There is a simple path between every pair of distinct vertices of a connected undirected graph.

8
Example Are the following graphs connected? c e f a d b g e c a f b d YesNo

9
Cut edges and vertices If one can remove a vertex (and all incident edges) and produce a graph with more connected components, the vertex is called a cut vertex. If removal of an edge creates more connected components the edge is called a cut edge or bridge.

10
Example Find the cut vertices and cut edges in the following graph. a b c d f e h g Cut vertices: c and e Cut edge: (c, e)

11
Connectedness in Directed Graphs A directed graph is strongly connected if there is a path from a to b and from b to a whenever a and b are vertices in the graph. A directed graph is weakly connected if there is a path between every pair of vertices in the underlying undirected graph. A directed graph is weakly connected iff there is always a path between two vertices when the direction are disregarded.

12
Example Is the following graph strongly connected? Is it weakly connected? a b c e d This graph is strongly connected. Why? Because there is a directed path between every pair of vertices. If a directed graph is strongly connected, then it must also be weakly connected.

13
Example Is the following graph strongly connected? Is it weakly connected? a b c e d This graph is not strongly connected. Why not? Because there is no directed path between a and b, a and e, etc. However, it is weakly connected.

Similar presentations

Presentation is loading. Please wait....

OK

CSE 211 Discrete Mathematics

CSE 211 Discrete Mathematics

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on as 14 amalgamation meaning Ppt on job rotation process Ppt on network security in ieee format Ppt on airport automation Ppt on product specification file Ppt on power generation through shock absorbers Ppt on generation of electricity from waste Ppt on taj mahal pollution Ppt on taj mahal tea Ppt on vegetarian and non vegetarian restaurant