On mixed metric dimension of flower and prism type graphs
Sunny Kumar Sharmasunnysrrm94@gmail.comSchool of MathematicsShri Mata Vaishno Devi UniversityKatra, Jammu and Kashmir, 182320, India0000-0001-9376-252XView full profile → , Yousef Al-Qudahy.alqudah@aau.edu.joalquyousef82@gmail.comDepartment of MathematicsFaculty of Arts and ScienceAmman Arab UniversityAmman, 11953, Jordan0000-0001-5952-4990View full profile → , *Vijay Kumar BhatCorresponding authorvijaykumarbhat2000@yahoo.comSchool of MathematicsShri Mata Vaishno Devi UniversityKatra, Jammu and Kashmir, 182320, India0000-0001-8423-9067View full profile →
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- Received:
- 01 Apr 2025
- Published Online:
- 30 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2602
- Pages:
- 2845–2862
Abstract
In this article, we consider two interesting classes of an infinite planar graphs (viz., the flower graph Sn = ℱn×3 and the graph Dn* , constructed using prism graph) and for these, we study a graph parameter, called the mixed metric dimension (MMD). We prove that both of these are the families of planar graphs with an unbounded and non-constant MMD. We also discuss the concept of an independent MMD and for these classes of infinite graphs, we show that the mixed metric basis set LM is independent. We also compare the results of MMD, with some of the already obtained results regarding the variants of metric dimension for these two planar graphs.
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References
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