  Based on a dendrimer graph theory, we investigate the ground state phase
diagrams of a nanostructure formed by three spins: $\sigma=1/2$, S=1 and q=3/2.
This nanostructure is built on a dendrimer with triangular core geometry. More
precisely, we evaluate the effect of different physical parameters including
the exchange interactions, the external magnetic and the crystal fields. By
varying these parameters, we analytically elaborate the ground state phase
diagrams. Concretely, we found that the existence of the crystal field
increases the number of stable phases. The total number of possible phases is
24=2x3x4, which are: ($\pm$1/2,$\pm$1,$\pm$3/2), ($\pm$1/2,0,$\pm$3/2),
($\pm$1/2,$\pm$1,$\pm$1/2) and ($\pm$1/2,0,$\pm$1/2). All these phases are
found to be stable, expect two special phases: (+1/2,0,-3/2) and (-1/2,0,+3/2),
which are masked by the other phases in all the ground state phase diagrams.
