Local Fractional Metric Dimensions of Generalized Petersen Networks

Abstract

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 $\mathbb GP(n,2)$ , where $n\geq 5$ . Moreover, for $n\in \{5, 8, 10\}$ exact values and for $n\in \{6, 7, 9, 11\}$ constant upper bounds of the LFMD are obtained. For $n\geq 12$ , the limiting values of LFMD for $\mathbb GP(n,2)$ are also obtained as 2 (bounded) if $n$ approaches to infinity.

Keywords

• Metric dimension
• local fractional metric dimension
• petersen network
• local resolving neighborhoods