I am having trouble trying to formulate a simple proof. I can clearly see that what I am trying to prove is correct but to prove it I am not sure what to do.
The problem is a broadcasting problem on a graph. My graph contains two cycles. The two cycles are joined by a single vertex $v$. If the vertex $v$ contains some info that it wants to broadcast to all other vertices on the graph what is the minimum number of rounds required to achieve this.
So a proof I am trying to formulate is that in order to achieve the minimum broadcast time I would have to first broadcast on the largest of the two cycles.
I was thinking of a proof by contradiction. Something like assume that we first broadcast on the smaller cycle and somehow show that it could lead to a broadcast time that is larger than the time if we were to start on the larger cycle.
To clarify, suppose we have two cycles $C_1$ and $C_2$ such that $|C_1| \ge |C_2|$. So the minimum broadcast time from vertex $v$ denoted by $b(v)$ would require us to broadcast on the larger cycle first.