B.D.Acharya和S.M.Hegde关于算术图一个猜想的证明

The proof to a conjecture on arithmetic graphs proposed by B.D.Acharya and S.M.Hegde

B.D.Acharya和S.M.Hegde猜想[1]:(1)、如果圈C_(4t+1)是(k,d)的算术图,那么必有k=2td+2r,其中r是某个非负整数;(2)如果圈C_(4t+3)是(k,d)算术图,则k=(2t+1)d+2r,其中r是某个非负整数。本文对以上猜想给出了肯定性证明。

In [1] B.D.Acharya and S.M.Hedge conjectured that (1). If circle C4t+1 is the arithmetic graph of(k,d), there must be k = 2td + 2r, where r is some non-negative integer; (2) if circle C4t+3 is the arithmetic graph of (k,d),then k = (2t + 1)d + 2r, where r is some non-negative integer; we give the proof to above conjecture in this article.