Abstract
A source detection problem in complex networks has been studied widely. Source localization has much importance in order to model many real-world phenomena, for instance, spreading of a virus in a computer network, epidemics in human beings, and rumor spreading on the internet. A source localization problem is to identify a node in the network that gives the best description of the observed diffusion. For this purpose, we select a subset of nodes with least size such that the source can be uniquely located. This is equivalent to find the minimal doubly resolving set of a network. In this article, we have computed the double metric dimension of convex polytopes R n and Q n by describing their minimal doubly resolving sets.
Highlights
Introduction and PreliminariesLet G be a finite and connected graph with vertex set VG and edge set EG. e cardinality of VG and EG is called the order and the size of the graph G, respectively
Despite of the fact that determining the minimal resolving sets of general graphs is computationally tough, the metric dimension has been gaining all the attention due to its applications in the different fields such as computer networking, navigation of robots, sonar technology, and optimization problems. e doubly resolving sets are a reasonable tool to successfully diagnose the source of infection within a network. e metric and double metric dimensions are NP-hard in general case
E focus of article was the computation of the double metric dimension regarding convex polytopes Rn and Qn
Summary
A source detection problem in complex networks has been studied widely. Source localization has much importance in order to model many real-world phenomena, for instance, spreading of a virus in a computer network, epidemics in human beings, and rumor spreading on the internet. A source localization problem is to identify a node in the network that gives the best description of the observed diffusion. For this purpose, we select a subset of nodes with least size such that the source can be uniquely located. Is is equivalent to find the minimal doubly resolving set of a network. We have computed the double metric dimension of convex polytopes Rn and Qn by describing their minimal doubly resolving sets
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