An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 i...An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G- e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e （x）. The existence of removable edges of k-connected graphs and some properties of 3-connected and 4-connected graphs have been investigated [1, 11, 14, 15]. In the present paper, we investigate some properties of 5-connected graphs and study the distribution of removable edges on a cycle and a spanning tree in a 5- connected graph. Based on the properties, we proved that for a 5-connected graph G of order at least 10, if the edge-vertex-atom of G contains at least three vertices, then G has at least （3│G│ ＋ 2）/2 removable edges.展开更多
基金Supported by the National Natural Science Foundation of China (No. 21101019)the Natural Science Foundation of Anhui Province University (No. KJ2009A122)+1 种基金the Chizhou College (2010RC005)the Materials Key Subject of Chizhou College (2011XK04)
文摘A novel interesting coordination polymer,[Cd（HSSA）（2-bimb）2].3H2O（1,H3SSA = 5-sulfosalicylic acid,2-bimb = 1,2-bis（imidazol-1-ylmethyl）-benzene）,has been synthesized and structurally characterized.Compound 1 crystallizes in the monoclinic system,space group P21/n with a = 10.8653（10）,b = 19.4100（17）,c = 17.4414（17） ,β = 91.944（2）°,V = 3676.2（6） 3,Z = 4,C35H38CdN8O9S,Mr = 859.19,Dc = 1.552 g/cm3,μ = 0.717 mm-1,S = 0.999,F（000） = 1760,R = 0.0531 and wR = 0.1078.The compound features a rare three-dimensional（3D） 5-connected nov topology.In addition,compound 1 exhibits strong photoluminescent emission at room temperature.
基金Supported by the National Natural Science Foundation of China (Grant No.10831001)the Science-TechnologyFoundation for Young Scientists of Fujian Province (Grant No.2007F3070)
文摘An edge e of a k-connected graph G is said to be a removable edge if G O e is still k-connected, where G e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G- e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e （x）. The existence of removable edges of k-connected graphs and some properties of 3-connected and 4-connected graphs have been investigated [1, 11, 14, 15]. In the present paper, we investigate some properties of 5-connected graphs and study the distribution of removable edges on a cycle and a spanning tree in a 5- connected graph. Based on the properties, we proved that for a 5-connected graph G of order at least 10, if the edge-vertex-atom of G contains at least three vertices, then G has at least （3│G│ ＋ 2）/2 removable edges.
