Abstract: A vertex irregular
total k-labeling of a graph G
is a labeling of vertices and edges of G
in such a way that for any different vertices x
and y, their weights and are distinct. The weight of a vertex x
is the sum of the label of x and the
labels of all edges incident with x.
The minimum k for which a graph G has a vertex irregular total k-labeling
is called the total vertex irregularity strength of G, denoted by In this paper, we determine the
total vertex irregularity strength of hexagonal graphs.
Keywords and phrases: total vertex irregularity strength, hexagonal graphs.
