A constructive method to determine the total vertex irregularity strength of two flower graph variants

Graph labeling is a well-established area of research in discrete mathematics. One notable variant is total vertex irregular labeling, which assigns labels to both vertices and edges such that the resulting vertex weights are all distinct. In this paper, we propose a constructive method to determine the total vertex irregularity strength of two flower graph variants, each characterized by only two distinct vertex degrees. Our approach involves assigning explicit labels and verifying that the resulting weighted degrees differ at every vertex. This method not only determines the exact total vertex irregularity strength for each graph but also introduces a replicable labeling strategy applicable to other graphs with similar structural features.