# lect20 - Graphs A graph consists of vertices connected by...

This preview shows pages 1–5. Sign up to view the full content.

1 Definition. A graph G =( V , E ) is an ordered pair of two sets V and E , where V is the (nonempty) set of vertices and E is the set of edges, each edge connects one vertex to the other (may be the same). E ={{ a , b }| a , b V }. Graphs. A graph consists of vertices connected by edges. 1 2 3 4 5 A graph having more then one edge between any two edges is called multigraph.

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

View Full Document
2 Sometimes, the edges of a graph have direction or orientation . Such directed edges are shown as arrows and the graph is then called a directed graph , or, a digraph . For directed graphs edges are ordered pairs, E ={( a , b )| a , b V }. 1) The results of a tournament of 6 teams can be represented as a digraph: vertices are teams and arrows represent the outcomes of the games. 1 is a a winner. 1 2 3 4 5 6 Examples
3 2) The dependency graph for computer programs. S 1 : a:=0 S 2 : b:=1 S 3 : c:=a+1 S 4 : d:=b+1 S 5 : e:=d+1 S 6 : e:=c+d S 1 S 2 S 3 S 6 S 4 S 5 3) The flow graph (flow of control) of the computer program (a digraph).

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

View Full Document
Definition. Two vertices u and v in an undirected graph G=( V , E ) are called adjacent if e ={ u , v } E Edge e is called incident with the vertices u and v , or u and v are endpoints of e . Definition. The number of times a vertex u is used as an endpoint of an edge is called the degree of u , deg ( u ). A self-loop contributes twice to the degree of the vertex.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

lect20 - Graphs A graph consists of vertices connected by...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online