The Modular Irregularity Strength of Triangular Book Graphs

This paper deals with the modular irregularity strength of a graph of  vertices, a new graph invariant, modified from the well-known irregularity strength, by changing the condition of the vertex-weight set associate to the irregular labeling from  distinct positive integer to -the group of integer modulo . Investigating the triangular book graph , we first find the irregularity strength of triangular book graph , which is also the lower bound for the modular irregularity strength, and then construct a modular irregular -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.