In this work, we study different types of dark energy (DE) models in the framework of the cosmographic approach, with emphasis on the running vacuum models (RVMs). We assess their viability using different information criteria and compare them with the so-called ghost DE models (GDEs) as well as with the concordance Lambda cold dark matter (CDM) model. We use the Hubble diagrams for Pantheon SnIa, quasars (QSOs), gamma-ray bursts (GRBs) as well as the data on baryonic acoustic oscillations (BAOs) in four different combinations. Upon minimizing the χ2 function of the distance modulus in the context of the Markov chain Monte Carlo method (MCMC), we put constraints on the current values of the standard cosmographic parameters in a model-independent way. It turns out that, in the absence of BAOs data, the various DE models generally exhibit cosmographic tensions with the observations at the highest redshifts (namely with the QSOs and GRBs data). However, if we include the robust observations from BAOs to our cosmographic sample, the CDM and RVMs are clearly favoured against the GDEs. Finally, judging from the perspective of the deviance information criterion (DIC), which enables us to compare models making use of the Markov chains of the MCMC method, we conclude that the RVMs are the preferred kind of DE models. We find it remarkable that these models, which had been previously shown to be capable of alleviating the σ8 and H0 tensions, appear now also as the most successful ones at the level of the cosmographic analysis.
