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The given figure represents a graph with 6 vertices and 7 edges.

The vertex set is {1, 2, 3, 4, 5, 6}.

The edge set is {(1,2), (1,3), (2,4), (2,5), (3,5), (4,6), (5,6)}.

The graph is connected as there is a path between every pair of vertices.

The degree of each vertex is as follows:

• Vertex 1 has degree 2
• Vertex 2 has degree 3
• Vertex 3 has degree 2
• Vertex 4 has degree 1
• Vertex 5 has degree 2
• Vertex 6 has degree 2