Total Vertex Irregularity Strength of Cubic and 4-Regular Graphs

Let $G$ be a graph and $k$ be a positive integer. A total $k$-labeling of $G$ assigns to each vertex and each edge a label from $\{1,\ldots,k\}$. The weight of a vertex is the sum of its label and the labels of its incident edges. A total labeling is vertex irregular if all vertex weights are distin