  We make use of the unprecedented depth, spatial resolution, and field of view
of the Euclid Early Release Observations of the Perseus galaxy cluster to
detect and characterise the dwarf galaxy population in this massive system. The
Euclid high resolution VIS and combined VIS+NIR colour images were visually
inspected and dwarf galaxy candidates were identified. Their morphologies, the
presence of nuclei, and their globular cluster (GC) richness were visually
assessed, complementing an automatic detection of the GC candidates. Structural
and photometric parameters, including Euclid filter colours, were extracted
from 2-dimensional fitting. Based on this analysis, a total of 1100 dwarf
candidates were found across the image, with 638 appearing to be new
identifications. The majority (96%) are classified as dwarf ellipticals, 53%
are nucleated, 26% are GC-rich, and 6% show disturbed morphologies. A
relatively high fraction of galaxies, 8%, are categorised as ultra-diffuse
galaxies. The majority of the dwarfs follow the expected scaling relations.
Globally, the GC specific frequency, S_N, of the Perseus dwarfs is intermediate
between those measured in the Virgo and Coma clusters. While the dwarfs with
the largest GC counts are found throughout the Euclid field of view, those
located around the east-west strip, where most of the brightest cluster members
are found, exhibit larger S_N values, on average. The spatial distribution of
the dwarfs, GCs, and intracluster light show a main iso-density/isophotal
centre displaced to the west of the bright galaxy light distribution. The ERO
imaging of the Perseus cluster demonstrates the unique capability of Euclid to
concurrently detect and characterise large samples of dwarfs, their nuclei, and
their GC systems, allowing us to construct a detailed picture of the formation
and evolution of galaxies over a wide range of mass scales and environments.
