construct a graph of order 5, whose vertices have degree 1,2,2,3,4. what is the size of this graph?
To create a graph with the given vertex degrees, we can follow these steps:
1. Start with a vertex of degree 4.
2. Connect this vertex to four other vertices to satisfy its degree.
3. Next, add a vertex of degree 3 and connect it to three other vertices.
4. Then, add two vertices of degree 2 and connect them each to two other vertices.
5. Finally, add a vertex of degree 1 and connect it to one other vertex.
This results in the following graph:
- Vertex 1 (Degree 4) connects to Vertices 2, 3, 4, 5
- Vertex 2 (Degree 3) connects to Vertices 1, 6, 7
- Vertex 3 (Degree 2) connects to Vertices 1, 8
- Vertex 4 (Degree 2) connects to Vertices 1, 9
- Vertex 5 (Degree 1) connects to Vertex 1
The size of the graph is the total number of edges, which can be calculated by summing up the degrees of each vertex and dividing by 2 (since each edge is counted twice).
Size = (4 + 3 + 2 + 2 + 1) / 2 = 6
Therefore, the size of this graph is 6.