A bond-additive connectivity index, named as the Mostar index, is used to measure the amount of peripheral edges of a simple connected graph, where a peripheral edge in a graph is an edge whose one end vertex has more number of vertices closer as compared to the other end vertex. In this study, we count the contribution of peripheral edges in commuting, non-commuting, and non-conjugate graphs associated to the dihedral and semi-dihedral groups. In fact, we compute the Mostar index of these graphs.