ON CONSTRUCTING $H$-IRREGULARITY LABELING WITH MINIMUM LABEL FOR CERTAIN BALLOON GRAPHS - Mila Mursalina; Yeni Susanti (Jurnal Matematika UNAND, 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.