On the total H-irregularity strength of corona product of a cycle and paths
M A Shulhany1*, Y Rukmayadi1, A Maharani1, A Agusutrisno1, R Rofiroh2, M F Haekal1, Y Utami1, B Lubis1, Z Syaifara1

1Faculty of Engineering, Universitas Sultan Ageng Tirtayasa, Jl. Jenderal Sudirman, KM. 3, Cilegon 42435, Banten, Indonesia
2Faculty of Engineering, Universitas Muhammadiyah Tangerang, Jl. Perintis Kemerdekaan I, No. 33, Tangerang 15118, Banten, Indonesia

Abstract

Let G be an undirected, simple, nontrivial, and finite graphs admitting an H covering. The total s labeling is called a total H irregular s labeling of G if for any pair of subgraphs have different weight. Define an H weight, denoted by omega of H, which sum of all edge and vertex labels in subgraph H 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. We study the ths of some graphs with Tdn covering.

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Topic: Mathematics