Use the graph to answer the following questions: a. Can there be a path of length bigger than 2 in the graph? Explain. b. Are there any non-trivial cycles in the graph? Explain. c. Give a trail of length 4. d. Give all self-loops in the graph.
Use the graph to answer the following questions: a. Can there be a path of length bigger than 2 in the graph? Explain. b. Are there any non-trivial cycles in the graph? Explain. c. Give a trail of length 4. d. Give all self-loops in the graph.
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Transcribed Image Text:**Graph Theory Question Analysis**
*3. Use the graph to answer the following questions:*
**a. Can there be a path of length bigger than 2 in the graph? Explain.**
- Yes, there can be a path of length greater than 2. For example, the path \( a \to c \to d \to e \) has a length of 3.
**b. Are there any non-trivial cycles in the graph? Explain.**
- Yes, there are non-trivial cycles in the graph. A non-trivial cycle is a cycle that involves more than one vertex. An example is \( a \to c \to a \).
**c. Give a trail of length 4.**
- A trail of length 4 is a walk where no edge is repeated. One example is \( a \to c \to d \to e \to f \).
**d. Give all self-loops in the graph.**
- The graph contains self-loops at nodes \( a \), \( b \), and \( e \).
**Graph Description:**
- The graph consists of seven vertices labeled \( a, b, c, d, e, f, \) and \( g \), with directed edges indicating possible paths. The self-loops are at vertices \( a \), \( b \), and \( e \). Direct connections exist between various vertices such as \( a \to g \), \( b \to a \), \( c \to d \), and more.
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