Graph Theory Quiz

Which of the following graphs is Eulerian?

• A graph with all vertices of even degree

• A graph with exactly two vertices of odd degree

• A graph with all vertices of odd degree

• A disconnected graph

What is the degree of a vertex in a graph?

• The number of edges connected to the vertex

• The number of vertices connected to the vertex

• The number of paths passing through the vertex

• The number of cycles containing the vertex

According to Euler's Theorem, a connected graph is Eulerian if and only if:

• It has exactly two vertices of odd degree

• All vertices have even degree

• It is a tree

• It has at least one vertex of odd degree

Which of the following statements is true for a Semi-Eulerian graph?

• It has all vertices of even degree

• It has exactly two vertices of odd degree

• It has more than two vertices of odd degree

• It is disconnected

If a graph has 5 vertices with degrees 2, 3, 3, 2, and 4, is it Eulerian, Semi-Eulerian, or neither?

• Eulerian

• Semi-Eulerian

• Neither

• Both

Which of the following is a necessary condition for a graph to have an Eulerian path?

• The graph must be connected

• The graph must be a tree

• The graph must have all vertices of even degree

• The graph must have no cycles

In a connected graph, if all vertices have even degree, what can be said about the graph?

• It has an Eulerian path

• It has an Eulerian circuit

• It is Semi-Eulerian

• It is a tree

How many vertices of odd degree must a graph have to be Semi-Eulerian?

• 0

• 1

• 2

• 3

Which of the following graphs is not connected?

• A graph with a single vertex

• A graph with a single edge

• A graph with multiple vertices and no edges

• A graph with multiple vertices and multiple edges

What is the sum of the degrees of all vertices in a graph with 6 edges?

• 6

• 12

• 18

• 24