On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs

Let G = (V(G), E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G) boolean OR E(G) -> {1, 2, ..., k} such that for each two edges ab and cd, it follows that f(a) + f(ab) + f(b) not equal f(c) + f(cd) + f(d), i.e. every two edges have distinct weights. The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength of graph G and denoted by tes(G). In this paper, we determine the exact value of total edge irregularity strength for staircase graphs, double staircase graphs and mirror-staircase graphs.