On the Total Irregularity Strength of Generalized Petersen Graph

As a standard notation, assume that G = G(V,E) is a finite, simple and undirected graph with p vertices and q edges. A labeling of a graph is any mapping that sends some set of graph elements to a set of numbers (usually positive integers). If the domain is the vertex-set or the edge-set, the labelings are called respectively vertex-labelings or edge-labelings. If the domain is V ∪E then we call the labeling a total labeling. In many cases it is interesting to consider the sum of all labels associated with a graph element. This will be called the weight of element. For a graph G we define a labeling φ : V ∪ E → {1, 2, . . . , k} to be a total k-labeling. A total k-labeling φ is defined to be an edge irregular total klabeling of the graph G if for every two different edges xy and x′y′ their weights φ(x) + φ(xy) + φ(y) and φ(x′) + φ(x′y′) + φ(y′) are distinct. Similarly, a total