Question

Graph Theory Question

Answer 1

http://gyazo.com/952ea8fd46198d73d2b3544d5423fb3e

Answer 2

I need help with (d)
I'm unable to find the Euler Circuit. Does it mean that it doesn't exist?

Answer 3

Because the vertex of \(u_1\) is of degree \(3\) which is odd?

Answer 4

A graph with more than 2 odd vertices does not contain any Euler path or circuit.

Answer 5

consider only the points u1, u2, v and x
there is no possible way to cover all of the paths in that corner only once, as you will always end up stuck at a point where you'll have to repeat an edge

Answer 6

So an euler circuit does not exists for this circuit because there degrees of the vertex are odd?

Answer 7

the degrees*

Answer 8

from what i've read, the hard and fast rules of Eulerian Circuits are:

A graph with all vertices being even contains an Euler circuit.
A graph with 2 odd vertices and some even vertices contains an Euler path.
A graph with more than 2 odd vertices does not contain any Euler path or circuit.

Answer 9

the only difference between a eulerian path and a eulerian circuit is that you have to end up where you started in a circuit

Answer 10

i dont think so, with euler path you dont need to end up where you started.

Answer 11

that's why i said "circuit"...

"the only difference between a eulerian path and a eulerian circuit is that you have to end up where you started in a \[circuit\] "

Answer 12

aite, thank you

Answer 13

welcome dude, as to ur earlier q, yeah, u1 has odd number of edges, u2 has odd number of edges, and u3 and u 4
so odd number > 2
so cant make path or circuit