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Chemical graph theory represents an interdisciplinary field at the intersection of chemistry and mathematics, focusing on the analysis of various chemical structures through graph-theoretical frameworks. This area facilitates the examination of complex and extensive chemical configurations by leveraging graph theory principles. In chemical structure graphs, atoms are depicted as vertices, with edges representing the bonds between them. By employing chemical graph theory, the exploration of diverse drug compounds and intricate molecular structures becomes more manageable. A key concept in this field is the resolvability parameter, a metric derived from graph theory. It stipulates that each vertex in a structure must possess a distinct representation via elected vertices, known as a metric basis, resolving set, or locating set in different scientific contexts. The metric dimension, defined as the minimum number of vertices in the resolving set, plays a crucial role in characterizing the structural properties of chemical graphs. In this study, we discussed the edge metric dimension of structures of benzodiazepines, alprazolam, chlordiazepoxide, clobazam, clonazepam, diazepam, nitrazepam, lolendazam, alferez, which are types of drug that used for the treatment of depression. We also put to use the edge metric dimension in anti-depression chemical structures, which are different types of Benzodiazepine. For application of this topic, we select the hospitals and health centers in any emergency situation. In any chronic disease situation, these chosen health centers provide all medical facilities to other hospitals efficiently only because we assigned each hospital and health center a unique code. |
