The star graph has recently been suggested as an alternative to the hy
percube. The star graph has a rich structure and symmetry properties a
s well as desirable fault-tolerant characteristics. The star graph's m
aximum vertex degree and diameter, viewed as functions of network size
, grow less rapidly than the corresponding measures in a hypercube. We
investigate the genus of the star graph and compare it with the genus
of the hypercube.