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On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs

Author

Listed:
  • Dalal Alrowaili
  • Zohaib Zahid
  • Imran Siddique
  • Sohail Zafar
  • Muhammad Ahsan
  • Muhammad Sarwar Sindhu

Abstract

Assume that G = (V(G), E(G)) is a connected graph. For a set of vertices WE⊆V(G), two edges g1, g2 ∈ E(G) are distinguished by a vertex x1 ∈ WE, if d(x1, g1) ≠ d(x1, g2). WE is termed edge metric generator for G if any vertex of WE distinguishes every two arbitrarily distinct edges of graph G. Furthermore, the edge metric dimension of G, indicated by edim(G), is the cardinality of the smallest WE for G. The edge metric dimensions of the dragon, kayak paddle, cycle with chord, generalized prism, and necklace graphs are calculated in this article.

Suggested Citation

  • Dalal Alrowaili & Zohaib Zahid & Imran Siddique & Sohail Zafar & Muhammad Ahsan & Muhammad Sarwar Sindhu, 2022. "On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6738129
    DOI: 10.1155/2022/6738129
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    References listed on IDEAS

    as
    1. Bao-Hua Xing & Sunny Kumar Sharma & Vijay Kumar Bhat & Hassan Raza & Jia-Bao Liu & Ali Ahmad, 2021. "The Vertex-Edge Resolvability of Some Wheel-Related Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, July.
    2. Changcheng Wei & Muhammad Salman & Syed Shahzaib & Masood Ur Rehman & Juanyan Fang & M. Irfan Uddin, 2021. "Classes of Planar Graphs with Constant Edge Metric Dimension," Complexity, Hindawi, vol. 2021, pages 1-10, April.
    3. Dalal Alrowaili & Zohaib Zahid & Muhammad Ahsan & Sohail Zafar & Imran Siddique & Gohar Ali, 2021. "Edge Metric Dimension of Some Classes of Toeplitz Networks," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, December.
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