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Distance-based dimensions provide the foreground for the identification of chemical compounds that are chemically and structurally different but show similarity in different reactions. The reason behind this similarity is the occurrence of a set S of atoms and their same relative distances to some ordered set T of atoms in both compounds. In this article, the aforementioned problem is considered as a test case for characterising the (molecular) graphs bearing the fractional metric dimension (FMD) as 1. For the illustration of the theoretical development, it is shown that the FMD of path graph is unity. Moreover, we evaluated the extremal values of fractional metric dimension of a tetrahedral diamond lattice. [ABSTRACT FROM AUTHOR]

The distance centric parameter in the theory of networks called by metric dimension plays a vital role in encountering the distance-related problems for the monitoring of the large-scale networks in the various fields of chemistry and computer science such as navigation, image processing, pattern recognition, 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, lesser number of the utilized nodes, and to characterize the chemical compounds, having unique presentations in molecular networks. After the arrival of its weighted version, known as fractional metric dimension, the rectification of distance-related problems in the aforementioned fields has revived to a great extent. In this article, we compute fractional as well as local fractional metric dimensions of web-related networks called by subdivided QCL, 2-faced web, 3-faced web, and antiprism web networks. Moreover, we analyse their final results using 2D and 3D plots. [ABSTRACT FROM AUTHOR]

Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots. [ABSTRACT FROM AUTHOR]

We demonstrate the ability of multidimensional Laplace NMR (LNMR), comprising relaxation and diffusion experiments, to reveal essential information about microscopic phase structures and dynamics of ionic liquids that is not observable using conventional NMR spectroscopy or other techniques. [ABSTRACT FROM AUTHOR]