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RosenCh7

RosenCh7 - Discrete Mathematics and Its Applications...

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1 Kenneth H. Rosen Chapter 7 Graphs Slides by Sylvia Sorkin, Community College of Baltimore County - Essex Campus Discrete Mathematics and Its Applications

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2 Definition 1. A simple graph G = (V, E) consists of V , a nonempty set of vertices , and E , a set of unordered pairs of distinct elements of V called edges . Simple Graph
3 A simple graph San Francisco Denver Los Angeles New York Chicago Washington Detroit How many vertices? How many edges?

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4 A simple graph V = { Chicago, Denver, Detroit, Los Angeles, New York, San Francisco, Washington } SET OF VERTICES E = { {San Francisco, Los Angeles}, {San Francisco, Denver}, {Los Angeles, Denver}, {Denver, Chicago}, {Chicago, Detroit}, {Detroit, New York}, {New York, Washington}, {Chicago, Washington}, {Chicago, New York} } SET OF EDGES
5 A simple graph San Francisco Denver Los Angeles New York Chicago Washington Detroit The network is made up of computers and telephone lines between computers. There is at most 1 telephone line between 2 computers in the network. Each line operates in both directions. No computer has a telephone line to itself. These are undirected edges, each of which connects two distinct vertices, and no two edges connect the same pair of vertices.

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6 Definition 2. In a multigraph G = (V, E) two or more edges may connect the same pair of vertices. A Non-Simple Graph
7 A Multigraph San Francisco Denver Los Angeles New York Chicago Washington Detroit THERE CAN BE MULTIPLE TELEPHONE LINES BETWEEN TWO COMPUTERS IN THE NETWORK.

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8 Multiple Edges San Francisco Denver Los Angeles New York Chicago Washington Detroit Two edges are called multiple or parallel edges if they connect the same two distinct vertices.
9 Definition 3. In a pseudograph G = (V, E) two or more edges may connect the same pair of vertices, and in addition, an edge may connect a vertex to itself. Another Non-Simple Graph

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10 A Pseudograph San Francisco Denver Los Angeles New York Chicago Washington Detroit THERE CAN BE TELEPHONE LINES IN THE NETWORK FROM A COMPUTER TO ITSELF (for diagnostic use).
11 Loops San Francisco Denver Los Angeles New York Chicago Washington Detroit An edge is called a loop if it connects a vertex to itself.

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12 Undirected Graphs pseudographs simple graphs multigraphs
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RosenCh7 - Discrete Mathematics and Its Applications...

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