Characterization of (Molecular) Graphs with Fractional Metric Dimension as Unity

Abstract

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.