For the subset S■V(G), if every path with k vertices in a graph G contains at least one vertex from S, we call that S is a k-path vertex cover set of the graph G. Obviously, the subset is not unique. The cardinality ...For the subset S■V(G), if every path with k vertices in a graph G contains at least one vertex from S, we call that S is a k-path vertex cover set of the graph G. Obviously, the subset is not unique. The cardinality of the minimum k-path vertex cover set of a graph G is called the k-path vertex cover number, we denote it by ψk(G). In this paper, a lower or upper bound of ψk for some Cartesian product graphs is presented.展开更多
利用出行特征数据识别综合交通运输通道是合理布局城市群综合运输通道的关键技术。本文基于城市群手机信令数据,提出一种综合运输通道识别四阶段方法框架,即数据准备、运输方式划分、最短路径搜索和通道识别。在运输方式划分方面,提出...利用出行特征数据识别综合交通运输通道是合理布局城市群综合运输通道的关键技术。本文基于城市群手机信令数据,提出一种综合运输通道识别四阶段方法框架,即数据准备、运输方式划分、最短路径搜索和通道识别。在运输方式划分方面,提出一种以运输平均速度和站点POI (Point of Interest)位置为决策变量的高速铁路、普速铁路和公路多方式划分算法。在最短路搜索方面,设计一种基于双向A*算法的最短路径搜索算法。在通道识别方面,基于行政边界划分通道区段并以运输量为综合运输通道区段判别参数。以京津冀城市群为例进行实证分析,结果表明,本文方法能够有效处理城市群手机信令数据,并识别出6条综合运输通道,验证了方法的可行性和准确性。在案例数据下,京津冀城市群公路和铁路的运输量占比分别为81.87%和18.13%,公路的短程运输客流较铁路更多;节假日因素显著提高了综合运输通道的客流量,平均运输量增加62.6%,平均客流周转量提升61.2%。展开更多
In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is c...In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.61463026,61463027).
文摘For the subset S■V(G), if every path with k vertices in a graph G contains at least one vertex from S, we call that S is a k-path vertex cover set of the graph G. Obviously, the subset is not unique. The cardinality of the minimum k-path vertex cover set of a graph G is called the k-path vertex cover number, we denote it by ψk(G). In this paper, a lower or upper bound of ψk for some Cartesian product graphs is presented.
文摘利用出行特征数据识别综合交通运输通道是合理布局城市群综合运输通道的关键技术。本文基于城市群手机信令数据,提出一种综合运输通道识别四阶段方法框架,即数据准备、运输方式划分、最短路径搜索和通道识别。在运输方式划分方面,提出一种以运输平均速度和站点POI (Point of Interest)位置为决策变量的高速铁路、普速铁路和公路多方式划分算法。在最短路搜索方面,设计一种基于双向A*算法的最短路径搜索算法。在通道识别方面,基于行政边界划分通道区段并以运输量为综合运输通道区段判别参数。以京津冀城市群为例进行实证分析,结果表明,本文方法能够有效处理城市群手机信令数据,并识别出6条综合运输通道,验证了方法的可行性和准确性。在案例数据下,京津冀城市群公路和铁路的运输量占比分别为81.87%和18.13%,公路的短程运输客流较铁路更多;节假日因素显著提高了综合运输通道的客流量,平均运输量增加62.6%,平均客流周转量提升61.2%。
文摘In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.
