The fractional versions of various metric related parameters have recently gained importance due to their applications in the fields of sensor networking, robot navigation and linear optimization problems. Convex polytopes are collection of those polytopes of Euclidean space which are their convex subsets. They have key importance in the field of network designing due to their stable and resilient structure which aids optimal data transfer. The identification and removal of components (nodes) of a communication network causing abruption in its flow is of key importance for optimal data transmission. These components are referred as strong resolving neighbourhood (SRNs) in graph theory and assigning least weight to these components aids the computation of fractional strong metric dimension (FSMD). In this paper, we compute FSMD for certain convex polytopes which include $\mathbb{P}_{n}$, $\mathbb{P}_{n}^{1}$ and $\mathbb{P}_{n}^{2}$. In this regard, it is shown that for $n \geq 3$, FSMD of $\mathbb{P}_{n}$ and $\mathbb{P}_{n}^{2}$ is $n$ and $\frac{3n}{2}$, respectively. Also, FSMD of $\mathbb{P}_{n}^{1}$ is $n$ when $n$ is odd and $\frac{3n}{2}$ when $n$ is even. Finally, an application of FSMD in the context of internet connection networks is furnished.
Jamil, F., Kashif, A., & Zafar, S. (2024). Fractional Strong Metric Dimension of Convex Polytopes and its applications. Hacettepe Journal of Mathematics and Statistics1-15. https://doi.org/10.15672/hujms.1211776
AMA
Jamil F, Kashif A, Zafar S. Fractional Strong Metric Dimension of Convex Polytopes and its applications. Hacettepe Journal of Mathematics and Statistics. Published online August 1, 2024:1-15. doi:10.15672/hujms.1211776
Chicago
Jamil, Faiza, Agha Kashif, and Sohail Zafar. “Fractional Strong Metric Dimension of Convex Polytopes and Its Applications”. Hacettepe Journal of Mathematics and Statistics, August (August 2024), 1-15. https://doi.org/10.15672/hujms.1211776.
EndNote
Jamil F, Kashif A, Zafar S (August 1, 2024) Fractional Strong Metric Dimension of Convex Polytopes and its applications. Hacettepe Journal of Mathematics and Statistics 1–15.
IEEE
F. Jamil, A. Kashif, and S. Zafar, “Fractional Strong Metric Dimension of Convex Polytopes and its applications”, Hacettepe Journal of Mathematics and Statistics, pp. 1–15, August 2024, doi: 10.15672/hujms.1211776.
ISNAD
Jamil, Faiza et al. “Fractional Strong Metric Dimension of Convex Polytopes and Its Applications”. Hacettepe Journal of Mathematics and Statistics. August 2024. 1-15. https://doi.org/10.15672/hujms.1211776.
JAMA
Jamil F, Kashif A, Zafar S. Fractional Strong Metric Dimension of Convex Polytopes and its applications. Hacettepe Journal of Mathematics and Statistics. 2024;:1–15.
MLA
Jamil, Faiza et al. “Fractional Strong Metric Dimension of Convex Polytopes and Its Applications”. Hacettepe Journal of Mathematics and Statistics, 2024, pp. 1-15, doi:10.15672/hujms.1211776.
Vancouver
Jamil F, Kashif A, Zafar S. Fractional Strong Metric Dimension of Convex Polytopes and its applications. Hacettepe Journal of Mathematics and Statistics. 2024:1-15.