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? (use a comma to separate answers as needed.)

Explanation:

Step1: Recall the condition for Euler circuit

A graph has an Euler circuit if and only if all vertices have even degrees.

Step2: Check the degrees of vertices

• Degree of \(A\): \(2\) (even)
• Degree of \(B\): \(4\) (even)
• Degree of \(C\): \(3\) (odd)
• Degree of \(D\): \(3\) (odd)
• Degree of \(E\): \(1\) (odd)
• Degree of \(F\): \(2\) (even)
• Degree of \(G\): \(3\) (odd)
• Degree of \(H\): \(3\) (odd)

We need to make all degrees even. Removing edges \(CE\) and \(DG\) (or other equivalent pairs that reduce the number of odd - degree vertices to \(0\)).

Answer:

\(CE,DG\)