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Think of the Internet as one big graph, where each web page is a vertex and each link is an edge. (a) Is this a directed graph? Why or why not? (b) Is this graph connected? Why or why not? (c) Is this graph complete? Why or why not? (d) Is this graph simple? Why or why not? (e) For a given web page p, what does the outdegree of p represent? (f) For a given web page p, what does the indegree of p represent? Consider the

Think of the Internet as one big graph, where each web page is a vertex and each link is an edge. (a) Is this a directed graph? Why or why not? (b) Is this graph connected? Why or why not? (c) Is this graph complete? Why or why not? (d) Is this graph simple? Why or why not? (e) For a given web page p, what does the outdegree of p represent? (f) For a given web page p, what does the indegree of p represent? Consider the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Does the following graph have an Euler path? Why or why not? 9. Consider the following graph. a # s 9 (a) Without adding new vertices, add a single edge to the graph so that the new graph will have an Euler path. Which vertices does your new edge connect? (b) In addition to the edge from part (a), add a second edge (using the existing vertices) so that the resulting graph will have an Euler circuit. Which vertices does your second new edge connect? 10. Think of the Internet as one big graph, where each web page is a vertex and each link is an edge. (a) Is this a directed graph? Why or why not? (b) Is this graph connected? Why or why not? (c) Is this graph complete? Why or why not? (d) Is this graph simple? Why or why not? (e) For a given web page p, what does the outdegree of p represent? (f) For a given web page p, what does the indegree of p represent? 11. Consider the graph in Example 2.3. The graph in Figure 2.4 shows a possible coloring using four colors. Explain why this graph cannot be colored using fewer than four colors,
Transcribed Image Text:8. Does the following graph have an Euler path? Why or why not? 9. Consider the following graph. a # s 9 (a) Without adding new vertices, add a single edge to the graph so that the new graph will have an Euler path. Which vertices does your new edge connect? (b) In addition to the edge from part (a), add a second edge (using the existing vertices) so that the resulting graph will have an Euler circuit. Which vertices does your second new edge connect? 10. Think of the Internet as one big graph, where each web page is a vertex and each link is an edge. (a) Is this a directed graph? Why or why not? (b) Is this graph connected? Why or why not? (c) Is this graph complete? Why or why not? (d) Is this graph simple? Why or why not? (e) For a given web page p, what does the outdegree of p represent? (f) For a given web page p, what does the indegree of p represent? 11. Consider the graph in Example 2.3. The graph in Figure 2.4 shows a possible coloring using four colors. Explain why this graph cannot be colored using fewer than four colors,
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