Motivated by some models of transmitting messages in interconnection networks,we studied a new parameter, named (d,4)-dominating number,in 2-dimensional toroidal mesh C(d1,d2).We show that the (d,4)-dominating number of C(d1,d2)(d1≥3,d2≥3) is 2 for d＝diam(G) or diam(G)+1.%本文讨论二维Toroidal网格的(d,4)-控制数,得到如下结果:(1)如果,m≥2,G＝C(2m+1)或G＝C(2m+2,3),当d＝diam(G)+1时,Rd,4(G)＝2;(2)如果G＝C(d1,4)(d1≥3)或G＝C(d15)(d1≥9),当d＝diam(G)时,Rd,4(G)＝2.
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