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Yeni Susanti
Department of Mathematics Universitas Gadjah Mada
Computer Science & IT Mathematics

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ON CONSTRUCTING $H$-IRREGULARITY LABELING WITH MINIMUM LABEL FOR CERTAIN BALLOON GRAPHS Mila Mursalina; Yeni Susanti
Jurnal Matematika UNAND Vol. 15 No. 3 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.3.346-357.2026

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.
Co-Authors Mila Mursalina