construct the graph of order 5, whose vertice have degrees 1,2,2,3,4. what is the size of this graph?
To construct a graph of order 5 with vertices of degrees 1, 2, 2, 3, and 4, we can arrange the vertices in the following way:
- Vertex 1 has degree 1
- Vertices 2 and 3 have degree 2
- Vertex 4 has degree 3
- Vertex 5 has degree 4
The resulting graph would look like this:
Vertex 1 ---- Vertex 2 ---- Vertex 4
/ /
Vertex 3 --- Vertex 5
This graph has a size of 5, as there are a total of 5 edges connecting the vertices.