摘要
The following results are obtained: (1) The graph Cm^m· Pt is odd arithmetic when (i) m ≡ 0 (mod 2) and t=m or m + 1; (ii) m ≡ 1 (mod 2) and t=m + 1. (2) The graph C2m^m is odd arithmetic when (i) m=2,4 and n is any positive integer; (ii) m=3 and n is even. (3) The graph Cm^m, is odd arithmetic when m=4n and t=2. (4) Pm+1^n is odd arithmetic when (i) n is odd; (ii) m 〈 3 and n is any positive integer. (5) Windmill graph Kn^t is odd arithmetic if and only if n=2. (6) Cycle Cn is odd arithmetic if and only if n ≡ 0 (mod 4). (7) For any positive integer n and any positive integer m, Km,n is odd arithmetic.
The following results are obtained: (1) The graph Cm^m· Pt is odd arithmetic when (i) m ≡ 0 (mod 2) and t=m or m + 1; (ii) m ≡ 1 (mod 2) and t=m + 1. (2) The graph C2m^m is odd arithmetic when (i) m=2,4 and n is any positive integer; (ii) m=3 and n is even. (3) The graph Cm^m, is odd arithmetic when m=4n and t=2. (4) Pm+1^n is odd arithmetic when (i) n is odd; (ii) m 〈 3 and n is any positive integer. (5) Windmill graph Kn^t is odd arithmetic if and only if n=2. (6) Cycle Cn is odd arithmetic if and only if n ≡ 0 (mod 4). (7) For any positive integer n and any positive integer m, Km,n is odd arithmetic.
基金
the Natural Science Foundation of Hebei Province and Mathematical Center (No. 08M002).