  In this paper, we explore the concept of total bondage in finite graphs
without isolated vertices. A vertex set $D$ is considered a total dominating
set if every vertex $v$ in the graph $G$ has a neighbor in $D$. The minimum
cardinality of all total dominating sets in $G$ is denoted as $\gamma_t(G)$. A
total bondage edge set $B$ is a subset of the edges of $G$ such that the
removal of $B$ from $G$ does not create isolated vertices, and the total
dominating number of the resulting graph $G-B$ is strictly greater than
$\gamma_t(G)$. The total bondage number of $G$, denoted $b_t(G)$, is defined as
the minimum cardinality of such total bondage edge sets. Our paper establishes
upper bounds on $b_t(G)$ based on the maximum degree of a graph. Notably, for
planar graphs with minimum degree $\delta(G) \geq 3$, we prove $b_t(G) \leq
\Delta + 8$ or $b_t(G) \leq 10$. Additionally, for a connected planar graph
with $\delta(G) \geq 3$ and $g(G) \geq 4$, we show that $b_t(G) \leq \Delta +
3$ if $G$ does not contain an edge with degree sum at most 7. We also improve
some upper bounds of the total bondage number for trees, enhance existing
lemmas, and find upper bounds for total bondage in specific graph classes.
