Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient condi...Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient conditions for A in the semigroup Gn(C) to be primitive are given. We also show that Gc(Jn) is a subsemigroup of Gn(C).展开更多
Let G =(Y, E) be a primitive digraph. The vertex exponent of G at a vertex v E V, denoted by expG(v), is the least integer p such that there is a v → u walk of length p for each u E V. We choose to order the vert...Let G =(Y, E) be a primitive digraph. The vertex exponent of G at a vertex v E V, denoted by expG(v), is the least integer p such that there is a v → u walk of length p for each u E V. We choose to order the vertices of G in such a way that expG(v1) ≤ expG(v2) ≤... ≤expG(vn). Then expG(vk) is called the k-point exponent of G and is denoted by expG(k), 1 〈 k 〈 n. We define the k-point exponent set E(n, k) := {expG(k)|G= G(A) with A E CSP(n)|, where CSP(n) is the set of all n × n central symmetric primitive matrices and G(A) is the associated graph of the matrix A. In this paper, we describe E(n, k) for all n, k with 1 〈 k 〈 n except n ≡ l(mod 2) and 1 〈 k 〈 n - 4. We also characterize the extremal graphs when k = 1.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
基金Supported by the National Natural Science Foundation of China(11071272,11101087)the Postdoctoral Science Foundation of China(2013M531785)+1 种基金the Natural Science Foundation of Fujian Province(2013J05006)the Foundation of Fuzhou University(2012-XQ-30)
文摘Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient conditions for A in the semigroup Gn(C) to be primitive are given. We also show that Gc(Jn) is a subsemigroup of Gn(C).
基金Foundation item:The NSF(04JJ40002)of Hunan and the SRF of Hunan Provincial Education Department.
文摘Let G =(Y, E) be a primitive digraph. The vertex exponent of G at a vertex v E V, denoted by expG(v), is the least integer p such that there is a v → u walk of length p for each u E V. We choose to order the vertices of G in such a way that expG(v1) ≤ expG(v2) ≤... ≤expG(vn). Then expG(vk) is called the k-point exponent of G and is denoted by expG(k), 1 〈 k 〈 n. We define the k-point exponent set E(n, k) := {expG(k)|G= G(A) with A E CSP(n)|, where CSP(n) is the set of all n × n central symmetric primitive matrices and G(A) is the associated graph of the matrix A. In this paper, we describe E(n, k) for all n, k with 1 〈 k 〈 n except n ≡ l(mod 2) and 1 〈 k 〈 n - 4. We also characterize the extremal graphs when k = 1.
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.