Let G be a finite group and D(G) be the degree pattern of G. Denote by h_{OD}(G) the number of isomorphism classes of finite groups H satisfying (H,D(H))=(G,D(G)). A finite group G is called kfold OD−characterizable if h_{OD}(G) = k. As the main results of this paper, we prove that each of the following pairs {G_{l}, G_{2}} of groups:
{B_{n}(q),C_{n}(q)}, n=2^{m} ≥ 2, π( 
q^{n}+1
2

=1 

q is odd prime power;
{B_{p}(3),C_{p}(3)}, π( 
3^{p}−1
2

=1 

p is an odd prime,
satisfies h_{OD}(G_{i}), i = 1,2. We also prove that, if (1)n = 2 and q is any prime power such
that
π([(q^{2}+1)/(2,q−1)])=1 or (2)n = 2^{m} ≥ 2 and q is a power of 2 such that
π(q^{n}+1)=1, then
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