A graph G is called a totally irregular total k-graph if it has a totally irregular total k-labeling λ : V ∪ E → {1, 2, • • • , k}, that is a total labeling such that for any pair of different vertices x and y of G, their weights wt(x) and wt(y) are distinct, and for any pair of different edges e and f of G, their weights wt(e) and wt(f ) are distinct. The minimum value k under labeling λ is called the total irregularity strength of G, denoted by ts(G). For special cases of a complete bipartite graph K m,n , the ts(K 1,n ) and the ts(K n,n ) are already determined for any positive integer n. Completing the results, this paper deals with the total irregularity strength of complete bipartite graph K m,n for any positive integer m and n.
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