Llex cornuta var.fortunei S.Y.Hu is a good ornamental tree species for viewing fruits and leaves,and has a wide range of garden uses.Nutrition bowl cutting seedlings can improve the survival rate of L.cornut a var.for...Llex cornuta var.fortunei S.Y.Hu is a good ornamental tree species for viewing fruits and leaves,and has a wide range of garden uses.Nutrition bowl cutting seedlings can improve the survival rate of L.cornut a var.fortunei S.Y.Hu transplanting and greening,and has the advantages of no time limit for planting and saving management costs.Based on this,this paper introduced the container seedling double-covering cutting technology for L.cornut a var.fortunei,to provide a reference for the propagation of L.cornut a var.fortunei.展开更多
Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let π ： X → Y be a double covering branched along a smooth divisor. We show that Jx is stable with respect to...Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let π ： X → Y be a double covering branched along a smooth divisor. We show that Jx is stable with respect to π＊H if the tangent bundle Jy is semi-stable with respect to some ample line bundle H on Y.展开更多
A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal i...A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).展开更多
In this paper, the authors discuss the upper bound for the genus of strong embeddings for 3-connected planar graphs on higher surfaces. It is shown that the problem of determining the upper bound for the strong embedd...In this paper, the authors discuss the upper bound for the genus of strong embeddings for 3-connected planar graphs on higher surfaces. It is shown that the problem of determining the upper bound for the strong embedding of 3-connected planar near-triangulations on higher non-orientable surfaces is NP-hard. As a corollary, a theorem of Richter, Seymour and Siran about the strong embedding of 3-connected planar graphs is generalized to orientable surface.展开更多
Let B（G） denote the bipartite double cover of a non-bipartite graph G with v ≥ 2 vertices and s edges. We prove that G is a perfect 2-matching covered graph if and only if B（G） is a 1-extendable graph. Furthermor...Let B（G） denote the bipartite double cover of a non-bipartite graph G with v ≥ 2 vertices and s edges. We prove that G is a perfect 2-matching covered graph if and only if B（G） is a 1-extendable graph. Furthermore, we prove that B（G） is a minimally l-extendable graph if and only if G is a minimally perfect 2-matching covered graph and for each e = xy ∈ E（G）, there is an independent set S in G such that ｜ГG（S）｜ = ｜S｜ ＋ 1, x ∈ S and ｜ГG-xy（S）｜ = ｜S｜ Then, we construct a digraph D from B（G） or G and show that D is a strongly connected digraph if and only if G is a perfect 2-matching covered graph. So we design an algorithm in O（x√vε） time that determines whether G is a perfect 2-matching covered graph or not.展开更多
The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X×K_(...The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X×K_(2).In this paper,integral generalized Cayley graphs on finite abelian groups are characterized,using the characterization of the spectra of integral Cayley graphs.As an application,the integral generalized Cayley graphs on Z_(p)×Z_(q) and Z2n are investigated,where p and q are odd prime numbers.展开更多
A classification of pentavalent symmetric graphs of order twice a prime square is given. It is proved that such a graph is a coset graph of Z3.A6 （non-split extension）, or a bi-coset graph of an extra-special group ...A classification of pentavalent symmetric graphs of order twice a prime square is given. It is proved that such a graph is a coset graph of Z3.A6 （non-split extension）, or a bi-coset graph of an extra-special group of order 125, or the standard double cover of a specific abelian Cayley digraph of order a prime square.展开更多
This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite cla...This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g 13 all these surfaces are simply-connected.展开更多
We introduce a method to compute the girth of knots, defined by Herne^ndez and Lin, using the Jones and Brandt-Lickorish-Millett-Ho polynomial. We determine the girth of all knots up to 10 crossings.
文摘Llex cornuta var.fortunei S.Y.Hu is a good ornamental tree species for viewing fruits and leaves,and has a wide range of garden uses.Nutrition bowl cutting seedlings can improve the survival rate of L.cornut a var.fortunei S.Y.Hu transplanting and greening,and has the advantages of no time limit for planting and saving management costs.Based on this,this paper introduced the container seedling double-covering cutting technology for L.cornut a var.fortunei,to provide a reference for the propagation of L.cornut a var.fortunei.
文摘Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let π ： X → Y be a double covering branched along a smooth divisor. We show that Jx is stable with respect to π＊H if the tangent bundle Jy is semi-stable with respect to some ample line bundle H on Y.
文摘A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).
文摘In this paper, the authors discuss the upper bound for the genus of strong embeddings for 3-connected planar graphs on higher surfaces. It is shown that the problem of determining the upper bound for the strong embedding of 3-connected planar near-triangulations on higher non-orientable surfaces is NP-hard. As a corollary, a theorem of Richter, Seymour and Siran about the strong embedding of 3-connected planar graphs is generalized to orientable surface.
基金Acknowledgements The authors would like to thank the referees very much for their careful reading and their very instructive suggestions which improve this paper greatly. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11201158）.
文摘Let B（G） denote the bipartite double cover of a non-bipartite graph G with v ≥ 2 vertices and s edges. We prove that G is a perfect 2-matching covered graph if and only if B（G） is a 1-extendable graph. Furthermore, we prove that B（G） is a minimally l-extendable graph if and only if G is a minimally perfect 2-matching covered graph and for each e = xy ∈ E（G）, there is an independent set S in G such that ｜ГG（S）｜ = ｜S｜ ＋ 1, x ∈ S and ｜ГG-xy（S）｜ = ｜S｜ Then, we construct a digraph D from B（G） or G and show that D is a strongly connected digraph if and only if G is a perfect 2-matching covered graph. So we design an algorithm in O（x√vε） time that determines whether G is a perfect 2-matching covered graph or not.
基金supported by the National Natural Science Foundation of China(No.12271311,12101410,12201414)Taishan Scholars Program of Shandong Province.
文摘The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X×K_(2).In this paper,integral generalized Cayley graphs on finite abelian groups are characterized,using the characterization of the spectra of integral Cayley graphs.As an application,the integral generalized Cayley graphs on Z_(p)×Z_(q) and Z2n are investigated,where p and q are odd prime numbers.
文摘A classification of pentavalent symmetric graphs of order twice a prime square is given. It is proved that such a graph is a coset graph of Z3.A6 （non-split extension）, or a bi-coset graph of an extra-special group of order 125, or the standard double cover of a specific abelian Cayley digraph of order a prime square.
文摘This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g 13 all these surfaces are simply-connected.
文摘We introduce a method to compute the girth of knots, defined by Herne^ndez and Lin, using the Jones and Brandt-Lickorish-Millett-Ho polynomial. We determine the girth of all knots up to 10 crossings.
