<![CDATA[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.]]>
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