Behavior under standard graph operations

Determine how the S-packing total chromatic number behaves under standard graph operations, including the Cartesian product, corona product, and Mycielskian construction, in terms of the S-packing total chromatic numbers of the input graphs.

Background

The paper establishes bounds and exact values for several graph classes but does not analyze how the invariant transforms under graph constructions. In particular, the relationship between the S-packing total chromatic number of an operation applied to graphs and the corresponding invariants of the input graphs is explicitly stated to be unknown.

References

Furthermore, it is not known how the $S$-packing total chromatic number behaves under standard graph operations such as the Cartesian product, the corona product, or the Mycielskian construction, in terms of the $S$-packing total chromatic numbers of input graphs.

— On $S$-packing total colorings  (2609.10107 - Ferme et al., 9 Sep 2026) in Section 7, Open problems