Context. The interaction of polycyclic aromatic hydrocarbons (PAHs) with vacuum ultraviolet (VUV) photons triggers the emission of the well-known aromatic infrared bands (AIBs), but other mechanisms, such as fragmentation, can be involved in this interaction. Fragmentation leads to selection effects that favor specific sizes and structures. Aims. Our aim is to investigate the impact of aliphatic bonds on the VUV photostability of PAH cations in a cryogenic and collisionless environment with conditions applicable for photodissociation regions (PDRs). Methods. The studied species are derived from pyrene (C 16 H 10 ) and coronene (C 24 H 12 ) and contain aliphatic bonds either in the form of methyl or ethyl sidegroups or of superhydrogenation. Their cations are produced by laser desorption ionization and isolated in the cryogenic ion cell of the PIRENEA setup, where they are submitted to VUV photons of 10.5 eV energy over long timescales (~1000 s). The parent and fragment ions are mass-analyzed and their relative intensities are recorded as a function of the irradiation time. The fragmentation cascades are analyzed with a simple kinetics model from which we identify fragmentation pathways and derive fragmentation rates and branching ratios for both the parents and their main fragments. Results. Aliphatic PAH derivatives are found to have a higher fragmentation rate and a higher carbon to hydrogen loss compared to regular PAHs. On the other hand, the fragmentation of PAHs with alkylated sidegroups forms species with peripheral pentagonal cycles, which can be as stable as, or even more stable than, the bare PAH cations. This stability is quantified for the main ions involved in the fragmentation cascades by the comparison of the fragmentation rates with the photoabsorption rates derived from theoretical photoabsorption cross sections. The most stable species for which there is an effective competition of fragmentation with isomerization and radiative cooling are identified, providing clues on the structures favored in PDRs. Conclusions. This work supports a scenario in which the evaporation of nanograins with a mixed aliphatic and aromatic composition followed by VUV photoprocessing results in both the production of the carriers of the 3.4 μm AIB by methyl sidegroups and in an abundant source of small hydrocarbons at the border of PDRs. An additional side effect is the efficient formation of stable PAHs that contain some peripheral pentagonal rings. Our experiments also support the role of isomerization processes in PAH photofragmentation, including the H-migration process, which could lead to an additional contribution to the 3.4 μm AIB.