The Total Edge Irregular Strengths of Union Graphs of K2,n

Nurdin Nurdin ( Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology)
Edy Tri Baskoro ( Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology)
Muhammad Salman Alfarisi Nawawi ( Combinatorial Mathematics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology)

Jurnal Matematika & Sains
Vol 11, No 3 (2006)

For a simple graph G = (V, E) with the vertex setV and the edge setV, a labeling l :V ÈE ® {1,2,...,k} is called an edge irregular total k-labelling of G if for any two different edges  e = e e1 e e2 and  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 ≥  1 and n ≥ 2 have been determined.