Prove that any graph with an Euler circuit is connected.

Prove that any graph with an Euler circuit is connected.

Given information:

any graph with an Euler circuit.

Calculation:

PROOF BY CONTRADICTION:

Let G be a graph that contains some Euler circuit E where e_i are the edges in G and v_i are the vertices in G ( i = 1, 2,…, n and n a positive integer).

Let us assume that G is not connected. Then there exists two vertices v and w such that there does not exists a walk between v and w.

Note that v and w need to be distinct, because else v is a walk from v to w...