It seems there was an issue generating the image. Let me describe how you can manually draw the multigraph based on the degrees 
{
1
,
1
,
4
,
5
,
6
,
7
}
{1,1,4,5,6,7}.

Steps to draw the multigraph:
Vertices: Draw 6 vertices, label them from 
𝑉
1
V 
1
​
  to 
𝑉
6
V 
6
​
 , and assign the following degrees:

𝑉
1
V 
1
​
  and 
𝑉
2
V 
2
​
  each with degree 1.
𝑉
3
V 
3
​
  with degree 4.
𝑉
4
V 
4
​
  with degree 5.
𝑉
5
V 
5
​
  with degree 6.
𝑉
6
V 
6
​
  with degree 7.
Edges: Start connecting the vertices:

Connect 
𝑉
1
V 
1
​
  and 
𝑉
6
V 
6
​
  with 1 edge.
Connect 
𝑉
2
V 
2
​
  and 
𝑉
5
V 
5
​
  with 1 edge.
Connect 
𝑉
3
V 
3
​
 , 
𝑉
4
V 
4
​
 , 
𝑉
5
V 
5
​
 , and 
𝑉
6
V 
6
​
  using multiple edges and loops:
For example, 
𝑉
6
V 
6
​
  can have several edges connected to 
𝑉
4
V 
4
​
 , and a loop (edge connecting 
𝑉
6
V 
6
​
  to itself) can be used to fulfill the degree requirement of 7.
Loops and Multiple Edges: Since it's a multigraph, use additional edges between vertices or loops to meet the degree conditions where necessary.









To manually draw the multigraph based on the given degrees {1, 1, 4, 5, 6, 7}, follow these detailed steps:

### **Step 1: Draw the Vertices**
- Draw 6 vertices and label them \( V_1 \) through \( V_6 \).
- Assign the degrees as follows:
  - \( V_1 \) and \( V_2 \) each with degree 1.
  - \( V_3 \) with degree 4.
  - \( V_4 \) with degree 5.
  - \( V_5 \) with degree 6.
  - \( V_6 \) with degree 7.

### **Step 2: Connect the Vertices**
- **Connect \( V_1 \) and \( V_6 \) with 1 edge.**
  - \( V_1 \) now has a degree of 1 (fulfilled).
  - \( V_6 \) now has a degree of 1, needing 6 more edges to fulfill its degree.

- **Connect \( V_2 \) and \( V_5 \) with 1 edge.**
  - \( V_2 \) now has a degree of 1 (fulfilled).
  - \( V_5 \) now has a degree of 1, needing 5 more edges to fulfill its degree.

### **Step 3: Add More Edges and Loops**
- **Connect \( V_3 \) to \( V_4 \) with 2 edges.**
  - \( V_3 \) now has a degree of 2, needing 2 more edges.
  - \( V_4 \) now has a degree of 2, needing 3 more edges.

- **Connect \( V_3 \) to \( V_6 \) with 2 edges.**
  - \( V_3 \) now has a degree of 4 (fulfilled).
  - \( V_6 \) now has a degree of 3, needing 4 more edges.

- **Connect \( V_4 \) to \( V_5 \) with 3 edges.**
  - \( V_4 \) now has a degree of 5 (fulfilled).
  - \( V_5 \) now has a degree of 4, needing 2 more edges.

- **Connect \( V_5 \) to \( V_6 \) with 2 edges.**
  - \( V_5 \) now has a degree of 6 (fulfilled).
  - \( V_6 \) now has a degree of 5, needing 2 more edges.

- **Add a loop to \( V_6 \).**
  - \( V_6 \) now has a degree of 7 (fulfilled).

### **Step 4: Final Check**
- \( V_1 \): Degree 1 (fulfilled).
- \( V_2 \): Degree 1 (fulfilled).
- \( V_3 \): Degree 4 (fulfilled).
- \( V_4 \): Degree 5 (fulfilled).
- \( V_5 \): Degree 6 (fulfilled).
- \( V_6 \): Degree 7 (fulfilled).

Your multigraph is now complete, with all vertices satisfying the required degrees.

---

Would you like a more detailed explanation of any of the steps? Here are some additional related questions:

1. What is the difference between a simple graph and a multigraph?
2. How are loops counted in the degree of a vertex?
3. Can you explain the concept of graph isomorphism?
4. What is the significance of the degree sequence in a graph?
5. How do Eulerian paths and circuits relate to the degrees of vertices in a graph?

**Tip:** When drawing multigraphs, remember that loops count as 2 towards the degree of the vertex they're connected to.

It seems there was an issue generating the image. Let me describe how you can manually draw the multigraph based on the degrees {1,1,4,5,6,7}.

Learn how to manually draw a multigraph with vertex degrees {1,1,4,5,6,7}. This solution explains the step-by-step process, including connecting vertices with edges, adding loops, and using multiple edges to fulfill degree requirements. Ideal for students studying graph theory at Grades 9-12 level.

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