For which of the following combinations of the degrees of vertices would the connected graph be Eulerian?Select one:a.1,2,3b.2,3,4c.2,4,5d.1,3,5

Question

For which of the following combinations of the degrees of vertices would the connected graph be Eulerian?

Select one:

a. 1, 2, 3
b. 2, 3, 4
c. 2, 4, 5
d. 1, 3, 5

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Solution

A connected graph is Eulerian if and only if all vertices of the graph have even degree. This means that the degree of each vertex (the number of edges connected to the vertex) must be an even number.

Let's examine each of the options:

a. 1,2,3 - This cannot be Eulerian because the degrees 1 and 3 are odd.

b. 2,3,4 - This cannot be Eulerian because the degree 3 is odd.

c. 2,4,5 - This cannot be Eulerian because the degree 5 is odd.

d. 1,3,5 - This cannot be Eulerian because all the degrees 1, 3, and 5 are odd.

So, none of the given combinations would result in an Eulerian graph.

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For which of the following combinations of the degrees of vertices would the connected graph be Eulerian?Select one:a.1,2,3b.2,3,4c.2,4,5d.1,3,5

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