Prove a graph is a tree

[Little_ID]

This is my first time posting, so please bear with me how the format is and the way it's written (english isn't my native language).


A graph with 23 Edges.
No vertex amount is given.
However, there were 3 different degrees, 4, 1 and 5.



I didn't know how to start with this one so I ended up drawing it. I found that if degree 4 has 2 vertex, degree 5 has 4 vertexand degree 1 has 18 vertex, it'll fufill the tree requirement (which says |E|= n -1, which in this case n is 24 = 4+18+2)

However, I proved this through just drawing it out on paper. I need help to understand how I can do it just through mathematical equation.

 

[Dr.Peterson]

A graph with 23 Edges.
No vertex amount is given.
However, there were 3 different degrees, 4, 1 and 5.

I didn't know how to start with this one so I ended up drawing it. I found that if degree 4 has 2 vertex, degree 5 has 4 vertexand degree 1 has 18 vertex, it'll fufill the tree requirement (which says |E|= n -1, which in this case n is 24 = 4+18+2)

However, I proved this through just drawing it out on paper. I need help to understand how I can do it just through mathematical equation.

Please quote the problem exactly and completely; if you are translating it, it would be good to show both the original and your translation. If there is any image associated, we'll want that, too. And I'd like to see the full statement of whatever theorems you are using.

Then, please show us the picture you drew, so we can be sure to understand what you are saying.

But as I understand it, you are trying to prove that any graph with 23 edges, whose vertex degrees are all either 1, 4, or 5, must be a tree. Is that right? What you describe sounds more like just trying to find a tree that fits the description, which is quite different.