Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Consider the following graph.

(b) How many trails are there from a to c?
(c) How many walks are there from a to c?
**Graph Description:** The graph consists of three vertices labeled \(a\), \(b\), and \(c\). There are five edges, labeled \(e_1\) through \(e_5\). The edges connect the vertices as follows: - \(e_1\), \(e_2\), and \(e_3\) connect vertices \(a\) and \(b\). - \(e_4\) forms a loop at vertex \(b\). - \(e_5\) connects vertices \(b\) and \(c\). **Questions and Answers:** (a) How many paths are there from \(a\) to \(c\)? - Answer: 4 ✔️ (b) How many trails are there from \(a\) to \(c\)? - Answer: 4 ❌ (c) How many walks are there from \(a\) to \(c\)? - Answer: There are potentially many walks, but the space is incomplete (indicated with ❌). **Explanation:** - **Paths** refer to sequences of edges that connect two vertices without repeating any vertices. - **Trails** refer to sequences where vertices can repeat, but edges cannot. - **Walks** allow both edges and vertices to be repeated.
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Transcribed Image Text:**Graph Description:** The graph consists of three vertices labeled \(a\), \(b\), and \(c\). There are five edges, labeled \(e_1\) through \(e_5\). The edges connect the vertices as follows: - \(e_1\), \(e_2\), and \(e_3\) connect vertices \(a\) and \(b\). - \(e_4\) forms a loop at vertex \(b\). - \(e_5\) connects vertices \(b\) and \(c\). **Questions and Answers:** (a) How many paths are there from \(a\) to \(c\)? - Answer: 4 ✔️ (b) How many trails are there from \(a\) to \(c\)? - Answer: 4 ❌ (c) How many walks are there from \(a\) to \(c\)? - Answer: There are potentially many walks, but the space is incomplete (indicated with ❌). **Explanation:** - **Paths** refer to sequences of edges that connect two vertices without repeating any vertices. - **Trails** refer to sequences where vertices can repeat, but edges cannot. - **Walks** allow both edges and vertices to be repeated.
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