In this paper, we consider the following open problem raised by H. Schneider in 1984. Qucstioa [1, Question 5.3]: Let A=M-N be a weak regular splitting of a singularM-matrix. Does the ineqality ind<sub>1</sub...In this paper, we consider the following open problem raised by H. Schneider in 1984. Qucstioa [1, Question 5.3]: Let A=M-N be a weak regular splitting of a singularM-matrix. Does the ineqality ind<sub>1</sub> (M<sup>-1</sup> N)≤ind<sub>0</sub>（A） hold in some interesting cases evenif p(M<sup>-1</sup> N)】1?展开更多
The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area net...The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems.Given the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed.展开更多
文摘In this paper, we consider the following open problem raised by H. Schneider in 1984. Qucstioa [1, Question 5.3]: Let A=M-N be a weak regular splitting of a singularM-matrix. Does the ineqality ind<sub>1</sub> (M<sup>-1</sup> N)≤ind<sub>0</sub>（A） hold in some interesting cases evenif p(M<sup>-1</sup> N)】1?
基金This work was supported by the Natural Science Foundation of Fujian Province(Grant No.A0510021)Science and Technology Three Projects Foundation of Fujian Province(Grant No.2006F5068)
文摘The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems.Given the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed.
