In this paper, firstly we obtain an estimation of lower bounds for singular value of matrix, moreover give the equivalent representation of matrix when attaining estimation of lower bounds, these results improved corresponding results in [1]-[4].
In this paper, the concept of a-connective diagonal dominant matrix according to circuit is introduced, and new conditions for H-matrices are obtained, corresponding results of [1]-[9] are improved and generalized.
一个 n 阶自补图 G 满足(1)当 n≡1(mod 4)对,对每一u∈V(G)皆有 d_G(u)=(n-1)/2;(2)当 n≡0(mod 4)时,d_G(u_i)=n/2,1≤i≤n/2,d_G(v_j)=n/2-1,1≤j≤n/2,这里 V(G)={u_1,…,u_(n/2),v_1,…,v_(n/2)},则称 G 为拟正则自补图,简称 q.r.s.c 图。本文证明了2n 阶(n-1)度正则连通图以及任意 n 阶(n≥5)q.r.s.c 图都是 H-图。
