Abstract A labeling of a
graph is a map that carries graph elements to the numbers (usually
positive or nonnegative integers). The most common choices of
domain are the set of all vertices (vertex labelings), the edge set
alone (edge labelings), or the set of all vertices and edges (total
labelings).
In many cases, it is interesting to consider the sum of all labels
associated with a graph element. It is called the weight of the
element: the weight of a vertex or the weight of an edge.
In this thesis, we consider a total klabeling as a labeling of the
vertices and edges of graph G with labels from the set f1; 2; : : :
; kg. A total klabeling is de ned to be an edge irregular total
klabeling of the graph G if edgeweights are di erent for all pairs
of distinct edges and to be a vertex irregular total klabeling of G
if vertexweights are di erent for all pairs of distinct vertices.
The minimum value of k for which the graph G has an edge irregular
total k labeling is called the total edge irregularity strength of
the graph G, tes(G). Analogously, the total vertex irregularity
strength of G, tvs(G), is de ned as the minimum k for which there
exists a vertex irregular total klabeling of G. In this thesis, we
present new results on the total edge irregularity strength and the
total vertex irregularity strength.
