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The packing chromatic number $\chi$ $\rho$ (G) of a graph G is the smallestinteger k such that its set of vertices V (G) can be partitioned into kdisjoint subsets V 1 ,. .. , V k , in such a way that every two distinctvertices in V i are at distance greater than i in G for every i, 1 $\le$ i$\le$ k. Recently, Balogh, Kostochka and Liu proved that $\chi$ $\rho$ is notbounded in the class of subcubic graphs [Packing chromatic number of subcubicgraphs, Discrete Math. 341 (2018), 474483], thus answering a questionpreviously addressed in several papers. However, several subclasses of cubic orsubcubic graphs have bounded packing chromatic number. In this paper, wedetermine the exact value of, or upper and lower bounds on, the packingchromatic number of some classes of cubic graphs, namely circular ladders, andso-called H-graphs and generalised H-graphs.

Packing colouring of some classes of cubic graphs