Local and strong metric dimension of families of alternate snake graphs
Sunny Pahalsunny.pahal08@gmail.comDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , *Sohan LalCorresponding authorsohan.lal@sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Vijay Kumar Bhatvijaykumarbhat2000@yahoo.comSchool of MathematicsShri Mata Vaishno Devi UniversityKatra, Jammu and Kashmir, 182320, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Dec 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3102
- Pages:
- 3485–3502
Abstract
Consider G = (V, E) be an undirected, non-trivial, simple, and connected graph with vertex set V(G) and edge set E(G). A subset ℛ ⊆ V(G) is called a local resolving set for G if, for every pair of adjacent vertices say u, v ∈ V(G)\ℛ, there exists a vertex t ∈ ℛ such that d(u, t) ≠ d(v, t). A vertex t is said to be strongly resolve two vertices u and v if, either v belongs to a shortest path connecting u and t, or u belongs to a shortest path connecting v and t. The minimum cardinality of a local resolving set is called the local metric dimension (LMD) of G, while the minimum cardinality of a strong resolving set is known as the strong metric dimension (SMD) of G. It is well known that the problem of determining these resolving sets is NP-complete and plays an important role in graph theory with many real-world applications, including transportation systems, robot navigation, and network analysis. In this paper, we determine the local and strong resolving sets for the families of alternate snake graphs and prove that each family possesses an independent resolving set with a cardinality of two.
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References
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