Let D(n,d)={A|A is an n×n primitive matrix with d positive diagonal elements}. Itis well known that γ(A)≤2n-d-1 for A∈D(n,d). Suppose D_1(n,d)={A∈D(n,d) |γ(A)=2n-d-1} is the set of extremal matrices in D(n,d...Let D(n,d)={A|A is an n×n primitive matrix with d positive diagonal elements}. Itis well known that γ(A)≤2n-d-1 for A∈D(n,d). Suppose D_1(n,d)={A∈D(n,d) |γ(A)=2n-d-1} is the set of extremal matrices in D(n,d). This paper gives a characteriza-tion of the set D_1(n,d).展开更多
This paper first establishes a distance inequality of the associated dia-graph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exp...This paper first establishes a distance inequality of the associated dia-graph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exponent set of central symmetric primitive matrices of order n is {1, 2,…, n - 1}. There is no gap in it.展开更多
文摘Let D(n,d)={A|A is an n×n primitive matrix with d positive diagonal elements}. Itis well known that γ(A)≤2n-d-1 for A∈D(n,d). Suppose D_1(n,d)={A∈D(n,d) |γ(A)=2n-d-1} is the set of extremal matrices in D(n,d). This paper gives a characteriza-tion of the set D_1(n,d).
基金Foundation item:The Scientific Research Foundations of Hunan Provincial Education Department(02C448)Hunan University of Science and Technology(E50128)
文摘This paper first establishes a distance inequality of the associated dia-graph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exponent set of central symmetric primitive matrices of order n is {1, 2,…, n - 1}. There is no gap in it.
