  The basic objective of this research work is to investigate the stucture of
BiHom-associative trialgebras.\,In this respect we build up one important class
of BiHom-trialgebras and determine properties of right, left and middle
operations in BiHom-associative trialgebras.\,We provide a classification of
$n$-dimensional BiHom-trialgebras for $n\leq3$.\,Relying upon the
classification result of BiHom-associative trialgebras, the derivations and
centroids of low-dimensional BiHom-associative trialgebras are
characterized.\,Certain properties of the centroids in light of
BiHom-associative trialgebras are reviwed the centroids of low-dimensional
BiHom-associative trialgebras are computed.
