Could someone help explain to me how I can figure out if the graphs given are Euler cycle or Euler path? Is it through trial and error?
Here are some examples:
Would appreciate any help.
Look at the number of odd-degree vertices in each graph...
Hope that helps.
a graph is Eulerian if its contains an Eulerian circuit, where Eulerian circuit is an Eulerian trail. By eulerian trail we mean a trail that visits every edge of a graph once and only once. now use the result that "A connectded graph is Eulerian if and only if every vertex of G has even degree." now you may distinguish easily. You must notice that an Eulerian path starts and ends at different vertices and Eulerian circuit starts and ends at the same vertex.