Question

draw a graph with the given characteristics. the graph has four even vertices. choose the correct answer below. a. graph with vertices a, b, c, d b. graph with vertices a, b, c, d c. graph with vertices a, b, c, d d. graph with vertices a, b, c, d e. such a graph is not possible

Explanation:

Step1: Recall the definition of an even vertex

A vertex is even if its degree (the number of edges incident to it) is an even number.

Step2: Calculate the degree of each vertex in option A

• Degree of \(A\): \(2\) (even)
• Degree of \(B\): \(2\) (even)
• Degree of \(C\): \(2\) (even)
• Degree of \(D\): \(4\) (even)

Step3: Check other options (for completeness)

• Option B: Vertices \(A\), \(B\), \(C\), \(D\) have degrees \(3\), \(3\), \(3\), \(3\) (all odd)
• Option C: Vertices \(A\) has degree \(3\) (odd)
• Option D: Vertex \(A\) has degree \(3\) (odd)

Answer:

A.