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 ei are the edges in G and vi 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...