An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u...An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.展开更多
The Internet of Moving Things is rapidly becoming a reality where intelligent devices and infrastructures are fostering real-time data sus-tainability in smart cities and advancing crowdsourced tasks to improve energy...The Internet of Moving Things is rapidly becoming a reality where intelligent devices and infrastructures are fostering real-time data sus-tainability in smart cities and advancing crowdsourced tasks to improve energy consumption,waste management,and traffic operations.These intelligent devices create a complex network scenario in which they often move together or in conjunction with one another to complete crowdsourced tasks.Our research premise is that mobility relationships matter when performing these tasks,and therefore,a graph model based on representing the changes in mobility relation-ships is needed to help identify the neighbour devices that are moving close to one another in our physical world but also seamlessly con-nected in their virtual world.We propose a bi-partite community mobility graph model for linking intelligent devices in both virtual and physical worlds,as well as reaching a trade-off between crowd-sourced tasks designed with explicit and implicit citizen participation.This paper aims to explore a bi-partite graph as a promising spatiotemporal representation of IoMT networks since changes in mobility relationships over time can indicate volunteer organisation at the device and community levels.The Louvain community detection method is proposed to find communities of intelligent devices to reveal a value conscious participation of citizens.The proposed bi-partite graph model is evaluated using a real-world scenario in transportation,confirming the main role of evolving communities in developing crowdsourcing IoMT networks.展开更多
基金The NSF (60673048) of China the NSF (KJ2009B002,KJ2009B237Z) of Education Ministry of Anhui Province.
文摘An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.
基金supported by the NSERC/Cisco Industrial Research Chair,Grant IRCPJ 488403-1.
文摘The Internet of Moving Things is rapidly becoming a reality where intelligent devices and infrastructures are fostering real-time data sus-tainability in smart cities and advancing crowdsourced tasks to improve energy consumption,waste management,and traffic operations.These intelligent devices create a complex network scenario in which they often move together or in conjunction with one another to complete crowdsourced tasks.Our research premise is that mobility relationships matter when performing these tasks,and therefore,a graph model based on representing the changes in mobility relation-ships is needed to help identify the neighbour devices that are moving close to one another in our physical world but also seamlessly con-nected in their virtual world.We propose a bi-partite community mobility graph model for linking intelligent devices in both virtual and physical worlds,as well as reaching a trade-off between crowd-sourced tasks designed with explicit and implicit citizen participation.This paper aims to explore a bi-partite graph as a promising spatiotemporal representation of IoMT networks since changes in mobility relationships over time can indicate volunteer organisation at the device and community levels.The Louvain community detection method is proposed to find communities of intelligent devices to reveal a value conscious participation of citizens.The proposed bi-partite graph model is evaluated using a real-world scenario in transportation,confirming the main role of evolving communities in developing crowdsourcing IoMT networks.
