On the k-tuple domination of de Bruijn and Kautz digraphs

In a digraph G, a vertex u is said to dominate itself and vertices v such that (u,v) is an arc of G. For a positive integer k, a k-tuple dominating set D of a digraph is a subset of vertices such that every vertex is dominated by at least k vertices in D. The k-tuple domination number of a given digraph is the minimum cardinality of a k-tuple dominating set of the digraph. In this letter, we give the exact values of the k-tuple domination number of de Bruijn and Kautz digraphs.     

Deadlock control of autonomous vehicle storage and retrieval systems via coloured timed Petri nets and digraph tools

This paper addresses the deadlock control problem for the autonomous vehicle storage and retrieval system (AVS/RS). For an AVS/RS with several autonomous vehicles running in bi-direction, deadlock control is one of the key issues in the implementation of AVS/RS. The cycle-deadlock is the main type of deadlock in AVS/RS. In the paper, the dynamic model of AVS/RS is investigated by using coloured timed Petri nets (CTPN). Based on the CTPN model, a route digraph is built to detect cycle-deadlock in AVS/RS with digraph tools; the necessary and sufficient conditions of deadlock-free are established. Moreover deadlock-free control policies are proposed, the critical state in deadlock free is also identified and FCFS policy is applied to solve it. Finally, a case study is given to validate the policies.     

基于碳足迹信息模型的产品低碳创新设计

为进一步缓解全球气候变暖,从源头降低产品生命周期碳排放的低碳设计日益成为产品设计的重要方向。基于对产品低碳设计过程中决策信息的构成及对应设计策略的研究,构建了一种融合碳足迹的产品低碳设计信息模型,并在分析低碳设计决策信息内涵的基础上提出了一种基于产品结构树和详细设计参数的双重递进碳足迹根源特征定位方法。该方法基于定性/半定量矩阵的简约式生命周期评估(streamlined life cycle assessment,SLCA)法对碳排放关键结构单元进行初筛,并采用赋权关联图方法定位低碳设计的关键特征和设计参数。针对设计参数矛盾,利用TRIZ冲突解决理论进行求解从而实现低碳设计目标。以手持吸尘器作为低碳创新设计案例,对所提方法的可行性和有效性进行了验证。     

有向图能量的广义Coulson型积分公式

对于一个有向图D,它的能量E(D)定义为对应邻接矩阵的所有特征值实部的绝对值之和.本文利用复分析的方法给出了有向图能量的一个广义Coulson型积分公式,通过这个公式建立了有向图的能量与有向图的特征多项式之间的联系.