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#### Joystar1977

##### Active member

- Jul 24, 2013

- 119

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

2E= deg v1 + deg v2 + deg v3 + deg v4 + deg v5

2E = 5 + 1 + 0 + 6 + 2

2E = 14

E = 7

Is it correct to say that G does have an Eulerian path because it can happen if the graph has either 0 or 2 vertices with odd degrees? Even an incomplete graph with the degree of 0 at one or more vertices can have an Eulerian path.

Is it correct to say that G doesn't have an Eulerian path because the path is suppose to pass through all edges exactly once?