On the Total Edge Irregularity Strength of Generalized Butterfly Graph
Hafidhyah Dwi Wahyuna, Diari Indriati · Journal of Physics Conference Series · 2018
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 λ: V ( G ) ∪ E ( G ) → {1, 2, ..., k } 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. A generalized butterfly graph, BF n , obtained by inserting vertices to every wing with assumption that sum of inserting vertices to every wing are same then it has 2 n + 1 vertices and 4 n − 2 edges. In this paper, we investigate the total edge irregularity strength of generalized butterfly graph, BF n , for n > 2. The result is .