discrete math

[analog cloud]

is this a eulerian trail

[digital coral]

Hi Yaz, just stopping by the channel, checking it out. I would like to help but don't want to step on toes. What makes a Eulerian trail vs Eulerian circuit?

[rain belfry]

eulerian trails start and finish at different vertices but use different vertices

eulerian circuits start and finish at the same vertices

so like a hamiltonian cycle

@analog cloud find degree of each vertice, if you get a pair of two odd nodes then it must be an eulerian trail due to euler's handshaking lemma.

so, B and D have a degree of 3, so it must start and end there in order to pass through each vertice once.

personally i think it's only an eulerian trail

[digital coral]

this is close, but not completely correct. There are more rules to an eulerian trail than that. What other condition(s) must be met for eulerian trail?

[rain belfry]

oh

it's not necessarily a hamiltonian cycle is it

there's no obligation for it to only meet every vertex once

[digital coral]

Yea not hamiltonian cycle...different rules

[rain belfry]

wait

there must be exactly 2 odd vertices with the rest even degrees right?

i think what i was referring to by pair of nodes being odd would be more valid for the route inspection problem

[digital coral]

Exactly

[rain belfry]

because with route inspection you can have 6 odd nodes and still traverse

[digital coral]

So in this case eulerian trail conditions are not met.

[rain belfry]

but are there not exactly two vertices that are odd? B and D are both of degree 3