Total Edge Irregularity Strength of Modified Book Graphs

Let G(V, E) be a graph with vertex set V and edge set E. A map of f from the union of a vertex set and edge sets to {1, 2, ... , k} such that for each different edge uv and u'v' have different weights is called an irregular total edge k-graph labeling G(V, E). The weight of the edge uv is the sum of the edge label uv, the vertex label u, and the vertex label v. The smallest k so that the graph G(V, E) can be labeled with the edge irregular total k labeling is called the total edge irregularity strength of G(V, E) and is denoted by tes(G). Book graphs B-d(G) have d copies of graph G with a common edge, and the common edge is the same fixed one in all copies of G. We modify the book graphs by replacing G with a wheel graph or a complete graph to obtain wheel book graphs or complete book graphs, respectively. In this paper, we determine the total edge irregularity strength of modified book graphs: wheel book graphs and complete book graphs.