On total edge irregularity strength of tadpole chain graph Tr(6, n)

Given a graph G ( V, E ) with a non-empty set of vertices V and a setof edges E . A total labelling f : V ∪ E → {1,2,…, k } is called an edge irregular total labeling if the weight of every edge is distinct. The weight of anedgee, under the total labeling f , is the sum of label of edgee and all labels of vertices that are incident to e . In other words, wt ( xy ) = f ( xy ) + f ( x ) + f ( y ). The total edge irregularity strength of G , denoted by tes ( G ) is the minimum k used to label graph G with the edge irregular total labeling. A tadpole chain graph of length r , denoted as T r (6, n ), is a chain graph that consists of tadpole graph T (6, n ) on each block. In this paper, we get t e s ( T r ( 6 , n ) ) = ⌈ ( 6 + n ) r + 2 3 ⌉ and construct an algorithm to find it.