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- Title
Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph.
- Authors
Liu, Jia-Bao; Zafari, Ali; Zarei, Hassan
- Abstract
Let Γ be a simple connected undirected graph with vertex set V Γ and edge set E Γ . The metric dimension of a graph Γ 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 W = w 1 , w 2 , ... , w k of vertices in a graph Γ and a vertex v of Γ , the metric representation of v with respect to W is the k -vector r v W = d v , w 1 , d v , w 2 , ... , d v , w k . If every pair of distinct vertices of Γ have different metric representations, then the ordered set W is called a resolving set of Γ. It is known that the problem of computing this invariant is NP-hard. In this paper, we consider the problem of determining the cardinality ψ Γ of minimal doubly resolving sets of Γ and the strong metric dimension for the jellyfish graph JFG n , m and the cocktail party graph CP k + 1 .
- Subjects
COCKTAIL parties; JELLYFISHES; GRAPH connectivity; UNDIRECTED graphs; ORDERED sets; METRIC geometry; GEOMETRIC vertices
- Publication
Complexity, 2020, p1
- ISSN
1076-2787
- Publication type
Article
- DOI
10.1155/2020/9407456