Graph Theory 05: Paths and Cycles III

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I continue discussing paths and cycles. I define the girth, circumference, and diameter of a graph, along with the distance between two vertices. I then prove that the girth of a graph that contains a cycle is at most twice its diameter + 1.
The material follows Diestel's "Graph Theory", section 1.3.
  1. Marius Furter
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I have doubts about the claim of the length of the two paths in a cycle at around 12:00... If you had a ring-like cycle of let's say 6 vertices, and you named them clockwise from 1 to 6. If you choose x=1 and y=3, length (P) would be 2 and length(Q) world be 4 if I'm not mistaken... So the claim wouldn't stand. The claim abs(length(p)-length (q))<=1 wouldn't be true for many such cases like choosing vertices 1, 5 and 2, 4 and so on. Am i missing something?

karen-