Questions: Given the graph: What is the least number of edges that must be duplicated to eulerize the graph? (Type the number into the space provided)

Transcript text: Given the graph: What is the least number of edges that must be duplicated to eulerize the graph? (Type the number into the space provided) $\square$

Solution

Solution Steps

Step 1: Determine the degree of each vertex

The degree of a vertex is the number of edges connected to it.

A: 2
B: 3
C: 2
G: 2
I: 2
D: 2
E: 3
F: 2

Step 2: Count the number of vertices with odd degree

Vertices with odd degree are B and E. Thus, there are two vertices with odd degree.

Step 3: Apply the eulerization theorem

A graph can be eulerized by duplicating edges if it has exactly two vertices of odd degree. The number of edges that need to be duplicated is calculated by finding a path connecting the two odd-degree vertices and duplicating the edges along that path.

One such path between B and E is simply the edge BE. Therefore, only the edge BE needs to be duplicated.