| Abstrak/Abstract |
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
0
v
0
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 Bd(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. |
