ON CONSTRUCTING H-IRREGULARITY LABELING WITH MINIMUM LABEL FOR CERTAIN BALLOON GRAPHS - Mila Mursalina; Yeni Susanti (Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang, 2026)
If ρ and H are simple, connected, undirected graphs, and ρ can be covered by an H-covering, then for a positive integer p, a total p-labeling φ on ρ is considered as a total H-irregular p-labeling if, for every subgraph K of ρ that is isomorphic to H, the weight of K (the sum of the labels of all vertices and edges of K) is a unique number. The smallest integer p for which graph ρ can be labeled with a total H-irregular p-labeling is called the total H-irregularity strength of graph G. This paper presents the exact total H-irregularity strength values for some particular graphs including balloon graphs, double balloon graphs, and double balloon ladder graphs.