In this paper, we derive interrelations of graph distance measures by means of inequalities. For this investigation we are using graph distance measures based on topological indices that have not been studied in this context. Specifically, we are using the well-known Wiener index, Randić index, eigenvalue-based quantities and graph entropies. In addition to this analysis, we present results from numerical studies exploring various properties of the measures and aspects of their quality. Our results could find application in chemoinformatics and computational biology where the structural investigation of chemical components and gene networks is currently of great interest.
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