On the total H-irregularity strength of graphs: A new notion
Ika Hesti Agustin, Dafik Dafik, Marsidi Marsidi, Ermita Rizki Albirri · Journal of Physics Conference Series · 2017
A total edge irregularity strength of G has been already widely studied in many papers. The total α -labeling is said to be a total edge irregular α -labeling of the graph G if for every two different edges e 1 and e 2 , it holds w ( e 1 ) ≠ w ( e 2 ), where w ( uv ) = f ( u ) + f ( uv ) + f ( v ), for e = uv . The minimum α for which the graph G has a total edge irregular α -labeling is called the total edge irregularity strength of G , denoted by tes ( G ). A natural extension of this concept is by considering the evaluation of the weight is not only for each edge but we consider the weight on each subgraph H ⊆ G . We extend the notion of the total α -labeling into a total H -irregular α -labeling. The total α -labeling is said to be a total H -irregular α -labeling of the graph G if for H ⊆ G , the total H -weights W ( H ) = ∑ v ∈ V ( H ) f ( v ) + ∑ e ∈ E ( H ) f ( e ) are distinct. The minimum α for which the graph G has a total H -irregular α -labeling is called the total H -irregularity strength of G , denoted by tHs ( G ). In this paper we initiate to study the tHs of shackle and amalgamation of any graphs and their bound.