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In chemical graph theory, topological indices play an important role and have various uses in quantitative structure-property relationships (QSPR) as well as quantitative structure-activity relationships (QSARs). The Hosoya index is one of them, performing a molecular descriptor in mathematical chemistry. Therefore, progressing with investigations requires computing the Hosoya index of distinct molecular graphs. This research presents a computational method for determining the Hosoya index of pericondensed benzenoid systems using the transfer matrix approach and the Hosoya vector.