Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths

Let Γ=(VΓ,EΓ) be a simple undirected graph with finite vertex set VΓ and edge EΓ. A total n-labeling α:VΓ∪EΓ→{1,2,…,n} is called irregular labeling on Γ if for any two different edges xy x′y′ in EΓ the numbers α(x)+α(xy)+α(y) α(x′)+α(x′y′)+α(y′) are distinct. The smallest positive integer n such that can labeled by irregularity strength of Γ. In this paper, we provide some asymmetric graphs symmetric graphs, namely generalized arithmetic staircase double-staircase as forms existing graphs. Moreover, give construction corresponding labelings.