Notes Written by
Michael Slate
for the week of April 15th - April 19th
Monday April 15th, 2002
A graph G=(V, E) is:
•
V - a set of vertices
•
E - set of edges connecting vertices in V
An edge E = (U, V) is a pair of vertices
V = {
A, B, C, D, E
}
E = {
(A, B), (A, C), (B, C), (C, D), (D, E), (C, E)
}
Graphs can model real life problems like:
•
Communication networks
•
Electronic Circuits
•
Transport Networks (i.e. streets, intersections, etc.)
•
Event Dependencies
Graph Terms
•
Adjacent Vertices - vertices connected by an edge
B, C, and D are adjacent to A
•
Degree of Vertex - number of adjacent vertices (The degree of A is 3)
Degree(V) = 2 * (number of edges)
•
Path - sequence of Vertices, V1, V2, V3.
..Vk so that consecutive vertices Vi and
V(i + 1 ) are adjacent.