Total edge irregularity strength of complete graphs and complete bipartite graphs

A total edge irregular k -labelling ν of a graph G is a labelling of the vertices and edges of G with labels from the set { 1 , … , k } in such a way that for any two different edges e and f their weights φ ( f ) and φ ( e ) are distinct. Here, the weight of an edge g = u v is φ ( g ) = ν ( g ) + ν ( u ) + ν ( v ) , i. e. the sum of the label of g and the labels of vertices u and v . The minimum k for which the graph G has an edge irregular total k -labelling is called the total edge irregularity strength of G . e determined the exact value of the total edge irregularity strength of complete graphs and complete bipartite graphs.