Edge number of 3-connected diameter 3 graphs

Let the decay number, ζ(G) be the minimum number of components of a cotree of a connected graph G. Let Ω be the collection of all 3-connected diameter 3 graphs. In this paper, we prove that if k is the minimum number such that q ≥ 2p - k for each (p,q)-graph G ε Ω, and 1 is the minimum number such that ζ(H) ≤ l - 1 for each graph H ε Ω, then k=l. Furthermore, we prove that k ≤ 11 and we find a 3-connected, diameter 3 graph with q = 2p - 8. So we have that 8 ≤ k ≤ 11 and we conjecture that k = 8.