The total H-irregularity strength of some graph classes
Ahmad Shulhany, Yazid Rukmayadi, Aprilia Maharani, Agusutrisno, Ceri Ahendyarti, Rofiroh, Muhammad Fadhiil Haekal, Yollanda Utami Sukma, Bachtiar Lubis, Zuhrainis Syaifara · AIP conference proceedings · 2022
Let G be an undirected, simple, nontrivial, and finite graphs admitting an H-covering. The total s-labeling a: V(G) ᴜ E(G) ➔ {1,2, …, s} is called a total H-irregular s-labeling of G if for any pair of subgraphs H'≅H and H''≅H, it holds ω(H') ≠ ω(H'') when H' ≠ H''. Define an H-weight, denoted by ω(H), which sum of all edge and vertex labels in subgraph H ⊆ G under the total s-labeling. The smallest positive integer s such that G has an H-irregular total s-labeling is the total H-irregularity strength of G, denoted by ths(G, H). A (n, 1)-tadpole graph is a graph on n+1 vertices and denoted by Tdn. In this paper, we find ths of of some graphs with Tdn-covering, i.e. generalized butterfly graphs, and eclipse graphs.