The synthesis and the catalysis in the HDS of DBT reaction of nanostructured self-supported catalyst containing MoS_2+x nanoplatelets have been investigated. Enhancement of higher activity observed in sulfide catalyst sample (d) with respect to the ex situ and in situ references is more closely related to the morphology change of particles (nanoplatelets). In this work, we suggest that certain structures present in model catalysts maybe related to low dimensional structures and present a theoretical study of two MoS₂ clusters (one made of 34 atoms/cluster and the second one made of 41 atoms/cluster), to these clusters seven sulfur atoms were randomly located at the surface of the sulfur layer, in order to simulate certain structures resembling arrow shaped nanoplatelets that were found in a High Resolution TEM analysis performed in some MoS₂ samples. Additionally, one of the goals is to enquire about the electronic properties presented in such structures when the clusters terminated as Moor S-edge and if it could be correlated to the catalyst behavior of these compounds. To the 34 atoms/cluster Mo-edge yielded metallic behavior while the second cluster the 41 atoms/ cluster S-edge yielded a semiconductor behavior with a forbidden energy gap E_g of the order of @ 3.6 eV between the Valence and Conductions bands respectively. Moreover, to the same clusters enunciated formerly, when the sulfur atoms were located at the surface of the S-layer, for the first cluster (34 atoms/cluster) yielded a more metallic behavior, while the second one (41 atoms/cluster) yielded an isolator behavior. Our results agree with the experimental and theoretical results presented by several groups in different laboratories arriving to the conclusion that the S-Mo-S Mo-edge arrow heads structures could be responsible to the enhancement of the catalytic activity on the MoS₂ studied samples.