Assertion: graph's vertex | /r/HasProperty | degree
Facets:
Source sentences:
text: if and only if all vertices of $G$ are of even degree, and a connected graph $G$ is Eulerian if and only if its edge set can be decomposed into cycles.
text: For instance, the vertices of the simple graph shown in the diagram all have a degree of 2, whereas the vertices of the complete graph shown are all of degree 3.