Total edge irregularity strength of some cycle related graphs

An edge irregular total k -labeling f : V ∪  E → 1,2, ..., k of a graph G = ( V,E ) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u'v' , their weights f ( u )+ f ( uv )+ f ( v ) and f ( u' )+ f ( u'v' )+ f ( v' ) are distinct. The total edge irregularity strength tes( G ) is defined as the minimum k for which the graph G has an edge irregular total k -labeling. In this paper, we determine the total edge irregularity strength of new classes of graphs C m @ C n , P m,n * and C m,n * and hence we extend the validity of the conjecture tes( G ) = max {⌈| E ( G )|+2)/3⌉, ⌈(Δ( G )+1)/2⌉}    for some more graphs.