Eulerian Paths

Ever tried drawing this diagram using a pencil without lifting your pencil?

Is it possible to draw Graph $A$ using a pencil without lifting your pencil?

Is it possible to draw Graph $B$ using a pencil without lifting your pencil?

Ok, but how do you know whether you can do so with some random graph?

We call such a graph Eulerian.

How to determine whether a graph is Eulerian?

If a graph has more than $2$ odd degree vertices, it's not Eulerian. Otherwise, it is.

Finally, as an exercise, determine whether the following graph is Eulerian.

Is the above picture a representation of an Eulerian graph?

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