Algorithmic Aspect on the Minimum (Weighted) Doubly Resolving Set Problem of Graphs

Lu, Changhong; Ye, Qingjie; Zhu, Chengru

doi:10.1007/978-3-030-27195-4_20

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2022

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“…Ahmad et al [33] have constructed the MD and MDRSs for the line graph of kayak paddle graphs. Lu et al [34] developed a linear-time approach for the MDRS problem of all graphs, where each block represents a cycle or complete graph. In the case of prism and Hamming graphs and some convex polytopes, the MDRSs have been derived in [35][36][37], respectively.…”

Section: Introductionmentioning

confidence: 99%

Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes

Ahmad

Alrowaili

Zahid

et al. 2022

Journal of Mathematics

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Source localization is one of the most challenging problems in complex networks. Monitoring and controlling complex networks is of great interest for understanding different types of systems, such as biological, technological, and complex physical systems. Modern research has made great developments in identifying sensors through which we can monitor or control complex systems. For this task, we choose a set of sensors with the smallest possible size so that the source may be identified. The problem of locating the source of an epidemic in a network is equivalent to the problem of finding the minimal doubly resolving sets (MDRSs) in a network. In this paper, we calculate the minimal doubly resolving sets (MDRSs) of some classes of convex polytopes in order to compute their double metric dimension (DMD).

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