Lecture2 - IE 495 Lecture 2 Reading for this lecture...

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IE 495 Lecture 2 August 31, 2000
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Reading for this lecture Primary Miller and Boxer, Chapter 5 Aho, Hopcroft, and Ullman, Chapter 1 Fountain, Chapter 4 Secondary Roosta, Chapter 2 Cosnard and Trystram, Chapters 4
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Interconnection Networks
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Aside: Introduction to Graphs A graph G = (V, E) is defined by two sets, a finite, nonempty set V of vertices (or nodes) and a set E V × V of edges . Example: A road network. The edges can be either ordered pairs or unordered pairs. If the edges are ordered pairs, then they are usually called arcs and the graph is called a directed graph . Otherwise, the graph is called undirected. See AHU, Section 2.3
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(Undirected) Graph Terms Vertices u and v are endpoints of the edge (u, v) . We say an edge e = (u, v) is incident to its endpoints. Two vertices u and v are adjacent if (u, v) E . The degree of a vertex is the number of edges incident to it (equivalently, the number of vertices adjacent to it). A path is a sequence of edges ( v 1 , v 2 ) , ( v 2 , v 3 ), ..., ( v n-1 , v n ) The length of such a path is n-1 .
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