  This paper deals with the modular irregularity strength of a graph of n
vertices, a new graph invariant, modified from the irregularity strength, by
changing the condition of the vertex-weight set associate to the well-known
irregular labeling from n distinct positive integer to Z_n-the group of integer
modulo n. Investigating the triangular book graph B_m^((3)), we first find the
irregularity strength of triangular book graph s(B_m^((3)) ), as the lower
bound for the modular irregularity strength, and then construct a modular
irregular s(B_m^((3)) )-labeling. The result shows that triangular book graphs
admit a modular irregular labeling and its modular irregularity strength and
irregularity strength are equal, except for a small case and the infinity
property.
