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) ∪ E(G) → {1, 2, ..., k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) 6= 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.