This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: NETWORK MODELS I A Graph or equivalently a Network consists of a set V called vetrices , of nodes, and a set A called the set of arcs . Deﬁnition: An arc is an ordered set (called directed) or unordered set (called undirected) of vertices, representing a possible direction. Deﬁnition: A sequence of arcs such that each arc has exactly one vertex in common with the earlier arcs is called a chain . A chain can be directed or undirected. Deﬁnition: A chain where the terminal node of each arc is the starting node of the next arc is called a path . A path can be directed or undirected. Saigal (U of M) IOE 310 1 / 17 NETWORK MODELS II Deﬁnition: A path that starts and ends with the same node is called a loop. A loop can be directed or undirected. Deﬁnition: A tree is a network consisting of subset of nodes and arcs such that the resulting network has no loops. Deﬁnition: A spanning tree is a network which is a tree consisting all the nodes of the network. Saigal (U of M) IOE 310 2 / 17 EXAMPLE OF A NETWORK I Saigal (U of M) IOE 310 3 / 17 SHORTEST PATH AND MIN SPANNING TREE PROBLEMS I An Example: A park has been set aside for limited access. Cars are not allowed into the park, and visitors are carried by trams and jeeps on...
View
Full
Document
This note was uploaded on 04/02/2008 for the course IOE 310 taught by Professor Saigal during the Spring '08 term at University of Michigan.
 Spring '08
 Saigal

Click to edit the document details