Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph

Jia-Bao Liu, Ali Zafari and Hassan Zarei

Complexity, 2020, vol. 2020, 1-7

Abstract:

Let be a simple connected undirected graph with vertex set and edge set . The metric dimension of a graph is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. For an ordered subset of vertices in a graph and a vertex of , the metric representation of with respect to is the - vector . If every pair of distinct vertices of have different metric representations, then the ordered set is called a resolving set of . It is known that the problem of computing this invariant is NP-hard. In this paper, we consider the problem of determining the cardinality of minimal doubly resolving sets of and the strong metric dimension for the jellyfish graph and the cocktail party graph .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:9407456

DOI: 10.1155/2020/9407456

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