A novel 2-D lead-containing hybrid compound, [（PbCl2）（μ-Pyz）1/2], （Pyz = pyrazine） 1, has been synthesized by the hydrothermal assembly of pyrazine with lead chloride. Elemental analysis and X-ray crystal struc...A novel 2-D lead-containing hybrid compound, [（PbCl2）（μ-Pyz）1/2], （Pyz = pyrazine） 1, has been synthesized by the hydrothermal assembly of pyrazine with lead chloride. Elemental analysis and X-ray crystal structure analyses were carded out for the structural determination and characterization of the title compound. Compound 1 crystallizes in orthorhombic, space group lbam, with a = 19.5558（18）, b = 7.1939（6）, c = 7.5449（6） A, V = 1061.44（16） .A^3, C2H2Cl2NPb, Mr= 318.14, Z = 8, Dc= 3.982 g/cm^3, μ = 32.63 mm^-1, F（000） = 1096.0, R = 0.0368 and wR = 0.0901 for 623 observed reflections （I 〉 2σ（I））.展开更多
An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinali...An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinality of a resolving set of G. A resolving set W for G is fault-tolerant if W\{v} is also a resolving set, for each v in W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we determine the metric dimension and fault-tolerant metric dimension problems for the graphs of certain crystal structures.展开更多
基金This work was supported by the National Natural Science Foundation of China (No. 20173063), the State Key Basic Research and Development Plan of China (001CB108906), and the NSF of Fujian Province (E0020001)
文摘A novel 2-D lead-containing hybrid compound, [（PbCl2）（μ-Pyz）1/2], （Pyz = pyrazine） 1, has been synthesized by the hydrothermal assembly of pyrazine with lead chloride. Elemental analysis and X-ray crystal structure analyses were carded out for the structural determination and characterization of the title compound. Compound 1 crystallizes in orthorhombic, space group lbam, with a = 19.5558（18）, b = 7.1939（6）, c = 7.5449（6） A, V = 1061.44（16） .A^3, C2H2Cl2NPb, Mr= 318.14, Z = 8, Dc= 3.982 g/cm^3, μ = 32.63 mm^-1, F（000） = 1096.0, R = 0.0368 and wR = 0.0901 for 623 observed reflections （I 〉 2σ（I））.
文摘An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinality of a resolving set of G. A resolving set W for G is fault-tolerant if W\{v} is also a resolving set, for each v in W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we determine the metric dimension and fault-tolerant metric dimension problems for the graphs of certain crystal structures.
