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 if P n(A(G))≥0, for any n, then G is called path positive graph. 若对任何n，Pn（A（G））≥0，则称G是道路正图。 短句来源 if Pn(A(G))≥0 for any n,then G is called the pathpositive graph. 若对任何n，Pn（A（G））≥0，则称G是道路正图。 短句来源
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 [s,t]-GRAPH [s,t]-图及其Hamilton性 短句来源 Let G be a graph of order n and k any positive integer with k 设G是一个顶点数为n的图，k为任意正整数且k≤n。 短句来源 and positive familyhistory. x_9阳性家族史为智力低下的4个危险因素。 短句来源 Has it positive action? 能否发挥其积极作用? 短句来源 For a graph G. 对于图G. 短句来源

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 positive graph
 In this paper, we prove that the set of all factorization indices of a completely positive graph has no gaps.
 The path polynomial P k(λ), k≥1, is the characteristic polynomial of the tridiagonal matrix with 1′s on the super and subdiagonals and zeros elsewhere; and P 0(λ)≡1. The adjacency matrix of a connected graph is any unreduced and symmetrical (0,1) matrix. It is of combinational significance to calculate their path polynomials. Denote the adjacency matrix of a graph G by A(G); if P n(A(G))≥0, for any n, then G is called path positive graph. In this paper, we completely describe the structure formulas... The path polynomial P k(λ), k≥1, is the characteristic polynomial of the tridiagonal matrix with 1′s on the super and subdiagonals and zeros elsewhere; and P 0(λ)≡1. The adjacency matrix of a connected graph is any unreduced and symmetrical (0,1) matrix. It is of combinational significance to calculate their path polynomials. Denote the adjacency matrix of a graph G by A(G); if P n(A(G))≥0, for any n, then G is called path positive graph. In this paper, we completely describe the structure formulas of path polynomials of trees H n for and k≥0 and n≥6; by the way, the tree H n, n 6, is path positive. 道路多项式Ｐｋ（λ）是上，下对角线元素是１，其它元素为０的ｋ阶方阵的特征多项式，ｋ≥１；记Ｐ０（λ）≡１。连通图的邻接矩阵是不可约的（０，１）一对称矩阵。这类矩阵的道路多项式的计算有重要的组合意义。图Ｇ的邻接矩阵记作Ａ（Ｇ）。若对任何ｎ，Ｐｎ（Ａ（Ｇ））≥０，则称Ｇ是道路正图。该文给出了对任何ｋ≥０，树Ｈｎ，ｎ≥６的邻接矩阵Ａ（Ｈｎ）的道路多项式Ｐｋ（Ａ（Ｈｎ））的表达式。树Ｈｎ，ｎ≥６，是道路正图。 The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product... The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively. 本文所讨论的积图是图的笛卡尔积，图的张量积，图的逻辑积和图的强直积四种积图．证明了：①如果Ｇ１和Ｇ２都是连通图，则积图中笛卡尔积，逻辑积和强直积都是道路正图．②图的张量积是道路正图的是图Ｇ１和Ｇ２是一个连通图，Ｇ１［或Ｇ２］有一个奇圈，且ｍａｘ｛λ１μ１，λｎμｍ｝≥２，其中λ１和λｎ［或μ１和μｍ］分别是图Ｇ１或Ｇ２的最大和最小特征值 The pathpolynomial Pk(λ),k≥1,is the characteristic polynomial of the tridiagonal matrix with 1′s on the super and subdiagonals and zeros elsewhere;and P0(λ)=1.The adjacency matrix of a connected graph is any unreduced and symmetrical (0,1)matrix.It is of combinational significance to calculate their pathpolynomials.The adjacency matrix of a graph G is denoted by A(G);if Pn(A(G))≥0 for any n,then G is called the pathpositive graph.In this paper,we completely describe the strucure formulas... The pathpolynomial Pk(λ),k≥1,is the characteristic polynomial of the tridiagonal matrix with 1′s on the super and subdiagonals and zeros elsewhere;and P0(λ)=1.The adjacency matrix of a connected graph is any unreduced and symmetrical (0,1)matrix.It is of combinational significance to calculate their pathpolynomials.The adjacency matrix of a graph G is denoted by A(G);if Pn(A(G))≥0 for any n,then G is called the pathpositive graph.In this paper,we completely describe the strucure formulas for pathpolynomials of stars Sn for any k≥0 and n≥5,with the stars Sn,n≥5,being pathpositive. 道路多项式Ｐｋ（λ）是上、下对角线元素是１，其它元素为０的ｋ阶方阵的特征多项式（ｋ≥１）；记Ｐ０（λ）＝１。连通图的邻接矩阵是不可约的（０，１）—对称矩阵，称这类矩阵的特征多项式为其道路多项式。这类道路多项式的计算有重要的组合意义。图Ｇ的邻接矩阵记作Ａ（Ｇ）。若对任何ｎ，Ｐｎ（Ａ（Ｇ））≥０，则称Ｇ是道路正图。本文给出了对任何ｋ≥０，星Ｓｎ（ｎ≥５）的邻接矩阵Ａ（Ｓｎ）的道路多项式Ｐｋ（Ａ（Ｓｎ））的表达式。星Ｓｎ（ｎ≥５），是道路正图。 << 更多相关文摘
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