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

For a simple graph G = ( V , E ) with the vertex setV and the edge setV , a labeling l : V E E ® {1,2,..., k } is called an edge irregular total k - labelling of G if for any two different edges e = e e 1 e e 2 and f = f 1 f 2 in E ( G ) we have wt ( e ) wt ( f ) where ( e ) = l ( e 1 ) + l ( e ) + l ( e 2 ). 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 mK 2,n -path and a graph mK 2, n for any positive integer m ≥  1 and n ≥ 2 have been determined .