lec0302

lec0302 - Undirected Graphs Graphs are composed of two...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Graphs are composed of two components: vertices and edges. Vertices are essentially points. (They are also referred to as nodes.) Typically, they will be labeled on a graph. In an undirected graph, edges are simply lines in between pairs of vertices. So, for example, in a graph with n vertices, the maximum number of edges is n C 2 = n(n-1)/2. This is the number of edges in a complete graph. A complete graph is a graph where there exists an edge between all pairs of vertices. We will define the degree of each vertex of a graph to be the number of edges that are incident to that vertex. A path in a graph is a sequence of edges that can be traversed one by one. (This essentially means that the endpoint of an edge in a path has to be the starting point of the next edge in the path.) It is permissible for a path to start and end in the same place. (Or, of course, start and end in different places.) A graph is connected if there exists a path in between all pairs of vertices. Here is an example of a undirected graph:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

lec0302 - Undirected Graphs Graphs are composed of two...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online