Thursday

August 28, 2014

August 28, 2014

Posted by **Joy** on Tuesday, August 6, 2013 at 7:58pm.

If the degrees of the vertices are 5, 1, 0, 6, 2, respectively, does G have an Eulerian path? Why or why not?

- Discrete Mathematics -
**MathMate**, Thursday, August 8, 2013 at 9:57pmAn Eulerian path is a path which passes through ALL edges exactly once.

This can happen if the graph has either 0 or 2 vertices with odd degrees.

So even an incomplete graph (with degree 0 at one or more vertices) can have an Eulerian path.

- Discrete Mathematics -
**Joy**, Friday, August 9, 2013 at 1:36pmMathMate: Is this correct then for the following problem:

Let G be a graph with the vertex set V = [v1, v2, v3, v4, v5). If the degrees of the vertices are 5, 1, 0, 6, 2, respectively, does G have an Eulerian path? Why or why not?

5 + 1 + 0 + 6 + 2 = 14

2E = 14

E = 7

Yes, this problem does have an Eulerian path because it can have an odd degree or an incomplete graph can have the degree of 0 at one or more of the vertices.

**Related Questions**

Discrete Mathematics - Let G be a graph with vertex set V = {v1, v2, v3, v4, v5...

Discrete Mathematics - Let G be a graph with vertex set V = { v1, v2, v3, v4, v5...

Discrete Mathematics - Let G be a graph with vertex set V = {v1, v2, v3, v4, v5...

Discrete Mathematics - Let G be a graph with vertex set V = { v1, v2, v3, v4, v5...

heelp math - A graph is constructed iteratively according to the following ...

Discrete Mathematics - Using Fleury's Algorithm in the graph to the bottom left...

Discrete Mathematics - Using Fleury's Algorithm in the graph to the bottom left...

Discrete Mathematics - 3.Does it matter if we join two vertices with a straight ...

Discrete Mathematics - Consider the complete graph with 5 vertices, denoted by ...

Math - Prove that a simple graph with n >_ 2 vertices must have atleast two ...