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The need to determine pseudoperipheral vertices arises from several graph-theoretical approaches for ordering sparse matrix equations. Results of two algorithms for finding such vertices, namely, the George-Liu and Kaveh-Bondarabady algorithms, are evaluated in this work along with a variant of the Kaveh-Bondarabady algorithm. Experiments among these three algorithms in conjunction with the Reverse Cuthill-McKee method suggest that the modified algorithm is a suitable alternative for reducing bandwidth of matrices that arise from specific application area, but it is dominated by the well-know George-Liu algorithm mainly when considering the computational times of the algorithms.