ON CONSTRUCTING $H$-IRREGULARITY LABELING WITH MINIMUM LABEL FOR CERTAIN BALLOON GRAPHS
Abstract
If $\varrho$ and $H$ are simple, connected, undirected graphs, and $\varrho$ can be covered by an $H$-covering, then for a positive integer $p$, a total $p$-labeling $\varphi$ on $\varrho$ is considered as a total $H$-irregular $p$-labeling if, for every subgraph $K$ of $\varrho$ 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 $\varrho$ 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.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Digital Image Processing Techniques
Publication details
- Journal / source
- Jurnal Matematika UNAND
- Publisher
- Universitas Andalas
- Volume
- 15
- Issue
- 3
- Pages
- 346–357
- Publication date
- 31 July 2026
- Language
- EN