Does $G$ have an Euler circuit??

Question

The set of the vertices of the graph $G$ is $V=\{ 0,1,2,3,4,5,6\}$. The vertices i and j are connected with an edge if and only if $|i-j| \mod 3 \in \{0,1 \}$.

Does $G$ have an Euler circuit??

I drawed the graph:

Answer 1

Hint: a connected graph has an Eulerian circuit iff all of its vertices have even degree. What is the degree of vertex 1?

Answer 2

You have an error at your graph.The edge $1-6$ shouln't exist,because $|1-6| \mod 3=5 \mod 3=2 \notin \{ 0,1\}$. Therefore,all the vertices have an even degree and so your graph $G$ has an Eulerian circuit.