Packing colouring of some classes of cubic graphs

The packing chromatic number chi(rho)(G) of a graph G is the smallest integer k such that its set of vertices V (G) can be partitioned into k disjoint subsets V-1,..., V-k, in such a way that every two distinct vertices in V-i are at distance greater than i in G for every i, 1 <= i <= k. Recently, it was proved in [J. Balogh, A. Kostochka and X. Liu, Discrete Math. 341 (2018), 474-483] that chi(rho) is not bounded in the class of subcubic graphs, thus answering a question previously addressed in several papers. However, several subclasses of cubic or subcubic graphs have bounded packing chromatic number. In this paper, we determine the exact value of, or upper and lower bounds on, the packing chromatic number of some classes of cubic graphs, namely circular ladders, and so-called H-graphs and generalised H-graphs.