Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, ...Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of Fk?(G)? , Rk?(G) , r-iterative graph ,Frk?(G)? and r-iterative graph , where k?≥2 and r?≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.展开更多
针对复杂结构条件下的零部件装配路径自动求解困难的问题,提出基于障碍和贪心规则的快速扩展随机树(Rapidly-exploring random tree,RRT)算法。该算法以基本RRT算法为基础,采用随机采样、终点采样、局部采样相结合的采样方式,利用目标...针对复杂结构条件下的零部件装配路径自动求解困难的问题,提出基于障碍和贪心规则的快速扩展随机树(Rapidly-exploring random tree,RRT)算法。该算法以基本RRT算法为基础,采用随机采样、终点采样、局部采样相结合的采样方式,利用目标零件与障碍物的碰撞面片法向量和碰撞点位置来引导随机树的扩展方向,在每个扩展方向上按贪心规则进行扩展,并提出先平移后旋转的扩展策略。对求解得到的初始装配路径,提出运用分段线性拟合的方法进行路径自动优化。设计并开发了装配路径求解软件原型系统,进行了算例测试和实例应用,结果验证了算法的高效可行。展开更多
文摘Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of Fk?(G)? , Rk?(G) , r-iterative graph ,Frk?(G)? and r-iterative graph , where k?≥2 and r?≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.
文摘针对复杂结构条件下的零部件装配路径自动求解困难的问题,提出基于障碍和贪心规则的快速扩展随机树(Rapidly-exploring random tree,RRT)算法。该算法以基本RRT算法为基础,采用随机采样、终点采样、局部采样相结合的采样方式,利用目标零件与障碍物的碰撞面片法向量和碰撞点位置来引导随机树的扩展方向,在每个扩展方向上按贪心规则进行扩展,并提出先平移后旋转的扩展策略。对求解得到的初始装配路径,提出运用分段线性拟合的方法进行路径自动优化。设计并开发了装配路径求解软件原型系统,进行了算例测试和实例应用,结果验证了算法的高效可行。
