The spin-spin correlation between sites (in general, m and n) on the tree was found to have a transition point when considered at the vertices (e.g. A and Ā, its reflection), their respective neighboring sites (such as B and its reflection), and between sites adjacent to the top and bottom extreme vertices of the two trees (e.g. A and B), as may be determined from ⟨ ⟨ s m s n ⟩ ⟩ = Z N − − 1 ( 0 , T ) [ cosh ⁡ ⁡ J ] N b 2 N ∑ ∑ l = 1 z g m n ( l ) t l where N b is equal to the number of bonds, g m n ( l ) t l is the number of graphs counted for odd vertices with even intermediate sites (see cited methodologies and references for detailed calculations), 2 N is the multiplicity resulting from two-valued spin possibilities and the partition function Z N is derived from ∑ ∑ { s } e − − β β H . (Note: s i is consistent with the referenced literature in this section and is equivalent to S i or σ σ i utilized above and in earlier sections; it is valued at ± ± 1 .) The critical temperature T C is given by T C = 2 ϵ ϵ k B [ ln ⁡ ⁡ ( γ γ + 1 ) − − ln ⁡ ⁡ ( γ γ − − 1 ) ] .