Modular Total H-Irregularity Strength of Graphs

We investigate the modular total H-irregularity strength, a modular variant of the total H-irregularity strength of graphs. We establish a sufficient condition under which these two graph invariants coincide. As applications of this result, we determine the exact values of the modular total H-irregularity strength for several graph families. In each case, the obtained value attains the corresponding lower bound, proving that the bound is sharp.