Local Fractional Metric Dimensions of Generalized Petersen Networks

• Main Authors: Mohsin Raza, Dalal Awadh Alrowaili, Muhammad Javaid
• Format: Article
• Language: English
• Published: IEEE 2021-01-01
• Series: IEEE Access
• Subjects: Metric dimension; local fractional metric dimension; petersen network; local resolving neighborhoods
• Online Access: https://ieeexplore.ieee.org/document/9430539/

Metric dimension is a distance-based tool that is used in the different fields of computer science and chemistry such as navigation, combinatorial optimization, pattern recognition, image processing, integer programming and formation of chemical compounds. In this paper, we study the latest type of metric dimension called as local fractional metric dimension (LFMD) and find its upper bounds for generalized Petersen networks <inline-formula> <tex-math notation="LaTeX">$\mathbb GP(n,2)$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$n\geq 5$ </tex-math></inline-formula>. Moreover, for <inline-formula> <tex-math notation="LaTeX">$n\in \{5, 8, 10\}$ </tex-math></inline-formula> exact values and for <inline-formula> <tex-math notation="LaTeX">$n\in \{6, 7, 9, 11\}$ </tex-math></inline-formula> constant upper bounds of the LFMD are obtained. For <inline-formula> <tex-math notation="LaTeX">$n\geq 12$ </tex-math></inline-formula>, the limiting values of LFMD for <inline-formula> <tex-math notation="LaTeX">$\mathbb GP(n,2)$ </tex-math></inline-formula> are also obtained as 2 (bounded) if <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> approaches to infinity.