Assume that G(V, E) is a graph with V and E as its vertex and edge sets, respectively. We have G is simple, connected, and undirected. Given a function λ from a union of V and E into a set of k-integers from 1 until k. We call the function λ as a totally irregular total k-labeling if the set of weights of vertices and edges consists of different numbers. For any u € V, we have a weight ***. Also, it is defined a weight ***. A minimum k used in k-total labeling λ is named as a total irregularity strength of G, symbolized by ts(G). We discuss results on ts of some caterpillar graphs in this paper. The results are *** for p,q greater than or equal to 3, while ****.
- caterpillar graph
- total irregularity strength
- totally irregular total k-labeling