On the total edge irregularity strength of three towers hanoi graph

Abstract

Let G(V, E) be a connected, simple, and undirected graph with vertex set V and edge set E. A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2, … k}. An edge irregular total k-labeling of a graph G is a total k-labeling such that the weights calculated for all edges are distinct. The weight of an edge uv in G, denoted by wt(uv), is defined as the sum of the label of u, the label of v, and the label of uv. The total edge irregularity strength of G, denoted by tes(G), is the minimum value of the largest label k over all such edge irregular total k-labelings. The three towers hanoi graph is the state graph for Tower of Hanoi problems with three towers. In this paper, we investigate the total edge irregularity strength of three towers hanoi graph for n ≥ 1. The result is .