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Metric dimension is one of the distance-based parameter which is frequently used to study the structural and chemical properties of the different networks in the various fields of computer science and chemistry such as image processing, pattern recognition, navigation, integer programming, optimal transportation models, and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, and lesser number of the utilized nodes and to characterize the chemical compounds having unique presentation in molecular networks. The fractional metric dimension being a latest developed weighted version of the metric dimension is used in the distance-related problems of the aforementioned fields to find their nonintegral optimal solutions. In this paper, we have formulated the local resolving neighborhoods with their cardinalities for all the edges of the convex polytopes networks to compute their local fractional metric dimensions in the form of exact values and sharp bounds. Moreover, the boundedness of all the obtained results is also proved. [ABSTRACT FROM AUTHOR]

The different distance-based parameters are used to study the problems in various fields of computer science and chemistry such as pattern recognition, image processing, integer programming, navigation, drug discovery, and formation of different chemical compounds. In particular, distance among the nodes (vertices) of the networks plays a supreme role to study structural properties of networks such as connectivity, robustness, completeness, complexity, and clustering. Metric dimension is used to find the locations of machines with respect to minimum utilization of time, lesser number of the utilized nodes as places of the objects, and shortest distance among destinations. In this paper, lower bound of local fractional metric dimension for the connected networks is improved from unity and expressed in terms of ratio obtained by the cardinalities of the under-study network and the local resolving neighbourhood with maximum order for some edges of network. In the same context, the LFMDs of prism-related networks such as circular diagonal ladder, antiprism, triangular winged prism, and sun flower networks are computed with the help of obtained criteria. At the end, the bounded- and unboundedness of the obtained results is also shown numerically. [ABSTRACT FROM AUTHOR]