On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs
Yeni Susanti, Dept. of Mathematics Universitas Gadjah Mada, Y. I. Puspitasari, Surakarta Indonesia, Husnul Khotimah · Iranian Journal of Mathematical Sciences and Informatics · 2020
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 :, 2, ..., k} such that for each two edges ab and cd, it follows that f (a) + f (ab) + f (b) = 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.