A vertex with degree 2 in a graph has an edge that loops around itself. The graph is therefore a cycle graph.
What is Euler circuit?
- Every edge of a graph is used precisely once in an Euler circuit. An Euler path has two distinct vertices where it begins and finishes. A vertex serves as the beginning and conclusion of an Euler circuit.
- In an Eulerian path, we pass over two unvisited edges with one end point, v, each time we visit a vertex. As a result, the degree of each middle vertex in the Eulerian Path must be even.
- Since any vertex can be the central vertex in an Eulerian cycle, all vertices must have an even degree.
- All of a graph G's vertices must be even if it has an Euler circuit. Or, to put it another way, G cannot have an Euler circuit if the number of odd vertices is more than 0.
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