# Does this graph have Eulerian circuit paths?

For this graph, do Eulerian circuit path exist or not? Basic definition A Euler circuit is a circuit that uses every edge of a graph exactly once. A Euler circuit starts and ends at the same vertex. As far as i know the B follows Eulerian circuit path while A is not, is it correct?

## 3 Answers

None of those graphs have an Eulerian circuit because they both have vertices of odd degree: $c,f$ in $A$ and $g,h$ in $B$.

• Can you please check this question, its also helpful for me – Aadnan Farooq A Dec 10 '15 at 16:58

No, you can't, its semi eulerian, if in a connected graph it is possible to traverese all edges exactly once and go back to the starting vertex, then its eulerian, a connected graph is eulerian iff all vertex degree is even.

• Can you please check this question, its also helpful for me – Aadnan Farooq A Dec 10 '15 at 16:58

both of these graphs are not eulerian. I explained why not.

• can we say Figure B as Eulerian? – Aadnan Farooq A Dec 10 '15 at 16:41