S-packing total colorings for other classical graph families

Determine the S-packing total chromatic numbers for classical graph families beyond complete bipartite graphs, finite and infinite paths, and cycles, for sequences S not restricted to the cases treated in the paper.

Background

The paper introduces the S-packing total chromatic number and determines it for complete bipartite graphs for arbitrary non-decreasing sequences S, and for finite paths, infinite paths, and cycles when S contains only the integers 1 and/or 2. The authors explicitly identify the extension of this analysis to other classical graph families as unresolved.