The Total Edge Irregular Strengths of Union Graphs of K2,n - Nurdin Nurdin; Edy Tri Baskoro; Muhammad Salman Alfarisi Nawawi (Jurnal Matematika & Sains, 2006)
For a simple graph G = (V, E) with the vertex setV and the edge setV, a labeling l :V ÃE Â® {1,2,...,k} is called an edge irregular total k-labelling of G if for any two different edges Â e = e e1 e e2 and Â f = f1 f2 in E (G) we have wt (e) wt (f ) where (e) = l (e1) + l (e ) + l (e2 ). The total edge irregular strengths tes (G) of G is the smallest positive integer k for which G has an edge irregular total k-labelling. In this paper, a dual of an edge irregular total klabelling is introduced. Beside that, the total edge irregular strengths of a graph mK2,n -path and a graph mK2,n for any positive integer m â¥ Â 1 and n â¥ 2 have been determined.