Question

modify the graph by removing the least number of edges so that the resulting graph has an euler circuit. then find an euler circuit for the modified graph. which edge(s) should be removed so that the resulting graph has an euler circuit? fg (use a comma to separate answers as needed ) there are several euler circuits for this graph that begin at vertex b. choose the answer below that describes one such euler circuit. a. b,c,e,h,c,g,h,b,g,d,a,f,g,d,b b. b,c,e,h,c,g,h,b,g,d,a,f,d,b c. b,c,e,h,c,g,h,b,g,d,a,d,f,g,d,b d. b,c,e,h,c,g,h,b,d,a,f,d,b

Explanation:

Step1: Analyze each option

For an Euler circuit, each edge is traversed exactly once.

• Option A: In the sequence \(B,C,E,H,C,G,H,B,G,D,A,F,G,D,B\), the edge \(G - F\) is not present in the modified graph (since we removed \(FG\) to get an Euler circuit). Also, the edge \(G - D\) is traversed twice.
• Option B: In the sequence \(B,C,E,H,C,G,H,B,G,D,A,F,D,B\), each edge is traversed exactly once.
• Option C: In the sequence \(B,C,E,H,C,G,H,B,G,D,A,D,F,G,D,B\), the edge \(G - D\) is traversed twice.
• Option D: In the sequence \(B,C,E,H,C,G,H,B,D,A,F,D,B\), the edge \(B - D\) is not a valid edge in the modified graph.

Answer:

B. \(B,C,E,H,C,G,H,B,G,D,A,F,D,B\)