For an Euler Circuit, you are required to use each edge exactly once and end up at the node you started with. You may pass through any node as many times as needed.
Hello again everyone!
With the Euler's Circuit, do I have to use all vertices and edges?
The question is: find a Euler's circuit in figure 11.44
I counted the degrees and they are all of even numbers. But I can't find my way finding a euler circuit using everything.
But I did this, I just made a subgraph into a euler's circuit.
Euler’s Theorem 1
If a graph has any vertices of odd degree, then it CANNOT have an EULER CIRCUIT.
AND
If a graph is connected and every vertex has even degree, then it has AT LEAST ONE EULER CIRCUIT (usually more). <--- when it says at least one euler circuit, so there are more circuits, but does it use all vertices and edges or not?
Thanks so much!
I just found out something.
a --> b --> c --> g --> k --> j --> i --> h -->d --> e --> i --> f -->j --> g --> b --> f --> e --> b --> d --> a
I visited some vertices twice but I believe I only passed each edge once.
Going back to my question:
With the Euler's Circuit, do I have to use all vertices and edges?
Vertices: you answered i can go through it as many times as I want.
Edges: you said that I missed the edges inside.
So in my understanding to have a Euler's circuit is to use all the edges in the graph, and not omit any edges like it would be a subgraph.