On total distance irregular labeling of families graph and corona product of graphs

We define [Formula: see text]. The labeling [Formula: see text] is called a distance vertex irregular total [Formula: see text]-labeling if any vertices have distinct weight which [Formula: see text] for any vertices in a graph [Formula: see text]. The weight of a vertex [Formula: see text] is defined as the sum of the labels of adjacent vertex and the labels of all edges incident on this vertex. The smallest [Formula: see text] for which such labeling exists is called the total distance vertex irregularity strength of [Formula: see text], denoted by tdis[Formula: see text]. In this paper, we investigated bounds of the total distance vertex irregularity strength of graphs and determined the exact value of tdis of families graphs and corona product.