On total H-irregularity strength of diamond ladder, three circular ladder, and prism graphs
D M O Suni, Dafik Dafik, I Made Tirta, Arika Indah Kristiana, Rosanita Nisviasari · Journal of Physics Conference Series · 2020
Abstract Let G be a graph with vertex set V and edge set E. A total labeling φ : V(G)∪E(G) → {1, 2, 3, …, α} is called a total α-labeling of a graph G. For the subgraph H ⊆ G under the total α-labeling, H-weight is defined as wtφ (H) = ∑ v∈V(H) φ(v) + ∑ e∈E(H) φ(e). A total α-labeling is called an H-irregular total α-labeling of the graph G if wtφ (H′) ≠ wtφ (H”) for any two distinct subgraphs H′ and H” isomorphic to H. 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 total H-irregularity strength of G and we have obtained the tHs of diamond ladder, three circular ladder and prism graphs.