what is the edge set?

[gm346]

Construct a simple graph with vertices T

U

V

W whose degrees are 3, 1, 1, 1
What is the edge set?

Thank you for your help!

 

[daon2]

The edge set is the set of edges of the graph. For example, if an undirected graph has vertices 1,2,3 with edges drawn between 1 and 2, and 1 and 3, the set of edges is {{1,2}, {1,3}}. So an edge for an undirected graph is a set consisting of one or two vertices. Simple graphs are those whose edges contain two vertices.

 

[HallsofIvy]

You are told that T has degree 3 so there must be 3 edges starting at T. Each of the other vertices has degree 1 so there must be exactly one edge going to each of them. There is one obvious way to set up that graph. But there is a very easy way to answer this- every edge must have two vertices so add up the number of vertices and divide by 2.