On the total irregularity strength of caterpillar with each internal vertex has degree three
Diari Indriati, Isnaini Anniswati Rosyida, Widodo Widodo · Journal of Physics Conference Series · 2018
Let G be a simple, connected and undirected graph with vertex set V and edge set E . A total k -labeling is defined as totally irregular total k -labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as , while the weight of edge xy is . A minimum k for which G has totally irregular total k -labeling is mentioned as total irregularity strength of G and denoted by ts( G ). This paper contains investigation of totally irregular total k -labeling and determination of their total irregularity strengths for caterpillar graphs with each internal vertex between two stars has degree three. The results are and for n > 4: