  In this work, we extend the catalog of low-surface brightness (LSB) galaxies,
including Ultra-Diffuse Galaxy (UDG) candidates, within $\approx 0.4R_{vir}$ of
the Hydra I cluster of galaxies, based on deep images from the VST Early-type
GAlaxy Survey (VEGAS). The new galaxies are found by applying an automatic
detection tool and carrying out additional visual inspections of $g$ and $r$
band images. This led to the detection of 11 UDGs and 8 more LSB galaxies. For
all of them, the cluster membership has been assessed using the color-magnitude
relation derived for early-type giant and dwarf galaxies in Hydra I. The UDGs
and new LSB galaxies found in Hydra I span a wide range of central surface
brightness ($22.7 \lesssim \mu_{0,g} \lesssim 26.5$ mag/arcsec$^2$), effective
radius ($0.6 \lesssim R_e \lesssim 4.0$ kpc) and color ($0.4 \leq g-r \leq 0.9$
mag), and have stellar masses in the range $\sim 5\times 10^6 - 2\times
10^8$M$_{\odot}$. The 2D projected distribution of both galaxy types is similar
to the spatial distribution of dwarf galaxies, with over-densities in the
cluster core and north of the cluster centre. They have similar color
distribution and comparable stellar masses to the red dwarf galaxies. Based on
photometric selection, we identify a total of 9 globular cluster candidates
associated to the UDGs and 4 to the LSB galaxies, with the highest number of
candidates in an individual UDG being three. We find that there are no relevant
differences between dwarfs, LSB galaxies and UDGs: the structural parameters
(that is surface brightness, size, colors, n-index) and GCs content of the
three classes have similar properties and trends. This finding is consistent
with UDGs being the extreme LSB tail of the size-luminosity distribution of
dwarfs in this environment.
