# Is it possible disconnected graph has euler circuit?

I have doubt !

Wikipedia says :

An Eulerian graph is one in which all vertices have even degree; Eulerian graphs may be disconnected.

What I know :

Defitition of an euler graph

"An Euler circuit is a circuit that uses every edge of a graph exactly once. ▶ An Euler path starts and ends at different vertices. ▶ An Euler circuit starts and ends at the same vertex."

According to my little knowledge "An eluler graph should be degree of all vertices is even, and should be connected graph".

I am asking :Is it possible disconnected graph has euler circuit ? If it is possible show an example .

EDITED : Here is my suplimentary problem , I voted for the anwser .

Which of the following graphs has an Eulerian circuit?

• Note that wikipedia says that Eulerian graphs may be disconnected not that every disconnected graph is Eulerian... – Michael Biro Aug 30 '15 at 13:13
• bliendly ,I beilieved that eluer graph must be connected . That's wrong. – 1 0 Aug 30 '15 at 13:17

Here we go: $$\huge\cdot\qquad\cdot$$
remember that $0$ is even. The circuit is the "empty circuit"
• @user4791206 My bad, the wikipedia definition cited in your link was false. As such, not every $2n$-regular graph is eulerian and not every graph with even degrees is eulerian (see $\Delta\quad\Delta$). Instead, an eulerian graph can only be disconnected if there is exactly one connected component consisting of more than one vertex (i.e. all "disconnected vertices" must be singleton). – AlexR Aug 30 '15 at 13:38