Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This p...Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.展开更多
Throughout this paper,D=（d<sub>1</sub>,d<sub>2</sub>,...,d<sub>n</sub>）denote a sequence of nonnegative inte-gers.We let（?）（D）denote the class of all graphs with degree sequen...Throughout this paper,D=（d<sub>1</sub>,d<sub>2</sub>,...,d<sub>n</sub>）denote a sequence of nonnegative inte-gers.We let（?）（D）denote the class of all graphs with degree sequence D,or equally,theclass of all symmetric（0,1）--matrices with trace 0 and row sum vector D.The structure matrix S=S（D） of D is a matrix of order n+1,whose entries展开更多
The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with...The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.展开更多
提出了异构无线传感器网络的最小转发连通覆盖问题,其目标是寻找一个满足以下要求的最小转发连通覆盖集(minimum relay-connecting set cover,简称MRCSC):1)活跃节点完全覆盖任务区域.从三角点阵排列可以获得节点数量近似最优的结论出发...提出了异构无线传感器网络的最小转发连通覆盖问题,其目标是寻找一个满足以下要求的最小转发连通覆盖集(minimum relay-connecting set cover,简称MRCSC):1)活跃节点完全覆盖任务区域.从三角点阵排列可以获得节点数量近似最优的结论出发,给出了节点随机部署策略下的位置点优化选取原则,该原则着重考虑了当出现相邻节点间距离偏离3rs的情形时,能够限制不规则性的传播,最终构成近似规则的三角点阵排列.2)所有活跃节点与转发骨干网连通.由于节点到达sink的路径可能较长,导致路径的数据成功转发率较低,因而不要求节点与sink的连通,而是至少存在一条到达骨干节点、较高数据转发率的路径,因此提出了转发连通验证和增强算法.理论分析和仿真实验表明,最小转发连通覆盖集的覆盖质量与OGDC算法接近,但在提高了转发连通率的同时也有效地控制了覆盖集的规模.展开更多
文摘Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.
基金Supported by National Natural Science Foundation of China(No.19971086)
文摘Throughout this paper,D=（d<sub>1</sub>,d<sub>2</sub>,...,d<sub>n</sub>）denote a sequence of nonnegative inte-gers.We let（?）（D）denote the class of all graphs with degree sequence D,or equally,theclass of all symmetric（0,1）--matrices with trace 0 and row sum vector D.The structure matrix S=S（D） of D is a matrix of order n+1,whose entries
文摘The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.
文摘提出了异构无线传感器网络的最小转发连通覆盖问题,其目标是寻找一个满足以下要求的最小转发连通覆盖集(minimum relay-connecting set cover,简称MRCSC):1)活跃节点完全覆盖任务区域.从三角点阵排列可以获得节点数量近似最优的结论出发,给出了节点随机部署策略下的位置点优化选取原则,该原则着重考虑了当出现相邻节点间距离偏离3rs的情形时,能够限制不规则性的传播,最终构成近似规则的三角点阵排列.2)所有活跃节点与转发骨干网连通.由于节点到达sink的路径可能较长,导致路径的数据成功转发率较低,因而不要求节点与sink的连通,而是至少存在一条到达骨干节点、较高数据转发率的路径,因此提出了转发连通验证和增强算法.理论分析和仿真实验表明,最小转发连通覆盖集的覆盖质量与OGDC算法接近,但在提高了转发连通率的同时也有效地控制了覆盖集的规模.
