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Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph

Author

Listed:
  • Jia-Bao Liu
  • Ali Zafari

Abstract

Let be a finite, connected graph of order of, at least, 2 with vertex set and edge set . A set of vertices of the graph is a doubly resolving set for if every two distinct vertices of are doubly resolved by some two vertices of . The minimal doubly resolving set of vertices of graph is a doubly resolving set with minimum cardinality and is denoted by . In this paper, first, we construct a class of graphs of order , denoted by , and call these graphs as the layer Sun graphs with parameters , , and . Moreover, we compute minimal doubly resolving sets and the strong metric dimension of the layer Sun graph and the line graph of the layer Sun graph .

Suggested Citation

  • Jia-Bao Liu & Ali Zafari, 2020. "Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph," Complexity, Hindawi, vol. 2020, pages 1-8, September.
    • Handle: RePEc:hin:complx:6267072
    DOI: 10.1155/2020/6267072
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    Cited by:

    1. Jia-Bao Liu & Ali Zafari, 2022. "Some Resolving Parameters in a Class of Cayley Graphs," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Muhammad Ahmad & Dalal Alrowaili & Zohaib Zahid & Imran Siddique & Aiyared Iampan, 2022. "Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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