prove that if a graph G contain an euler circuit then G is c

prove that if a graph G contain an euler circuit, then G is connected

Solution

Given that G contains an Euler Circuit.

By definition, An Euler circuit is a circuit that uses every edge of a graph exactly once. Hence, there will be a path between every pair of vertices. Hence, there is no unreachable vertices. This is the definition of connectedness of a graph.

In another way of explanation, if a graph is not connected , then it cannot contain a circuit.