A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and numb...A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if for any cut-set , then G has a k-tree.展开更多
A temperature phase transformation stress coupled 3D nonlinear mathematical model has been proposed for forecasting distortion of workpieces on the cooling processes in this paper. Moreover, a series of subroutines we...A temperature phase transformation stress coupled 3D nonlinear mathematical model has been proposed for forecasting distortion of workpieces on the cooling processes in this paper. Moreover, a series of subroutines were developed on the MARC (analysis research corporation) software platform and the simulation result is basically identical with the experimental one that measured on the workpiece shape with LEITZ equipment. This verifies that the mathematical model and method are feasible.展开更多
Abstract The paper proves that if G is a k tree, then the bandwidth B(G) of the complement G of G is given by B(G)=n-k-1, when GK k+K n-k , n-k-2, otherwise.
文摘A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if for any cut-set , then G has a k-tree.
基金The work was supported by the National Natural Science Foundation of China(Grant No.50075053).
文摘A temperature phase transformation stress coupled 3D nonlinear mathematical model has been proposed for forecasting distortion of workpieces on the cooling processes in this paper. Moreover, a series of subroutines were developed on the MARC (analysis research corporation) software platform and the simulation result is basically identical with the experimental one that measured on the workpiece shape with LEITZ equipment. This verifies that the mathematical model and method are feasible.
文摘Abstract The paper proves that if G is a k tree, then the bandwidth B(G) of the complement G of G is given by B(G)=n-k-1, when GK k+K n-k , n-k-2, otherwise.
