Does this graph have Eulerian circuit paths?
Matthew Harrington 
$\begingroup$
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?
$\endgroup$3 Answers
$\begingroup$None of those graphs have an Eulerian circuit because they both have vertices of odd degree: $c,f$ in $A$ and $g,h$ in $B$.
$\endgroup$ 1 $\begingroup$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.
$\endgroup$ 1 $\begingroup$both of these graphs are not eulerian. I explained why not.
$\endgroup$ 1
