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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...
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 Spring '08
 Saigal
 Graph Theory, Shortest path problem, Flow network, IOE, Saigal

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