Linear high molecular weight polymers undergo central scission in strong flows due to buildup of stress from fluid drag. An alternative to linear architecture is the star branched polymer that shows higher shear stability against such scission. We consider two six-arm star polymers differing in the connectivity of the arms at the core. The first is a fused-core star PMMA, where the arms are interconnected at a triphenylene core, with the multiple bonds therein supporting one another against possible tensile fracture. The second is a linear-core star PMMA, containing linearly linked single bonds within the core as potential fracture sites under tensile stress. Their stress-induced scission tendency is analyzed during planar elongational flow of their dilute solutions in dibutyl phthalate in a cross-slot flow cell. We find that scission of the star PMMA at the arms dominates their degradation behavior, and both the linear-core and fused-core star PMMAs show similar flow-induced scission. These results are analyzed first in terms of the critical-stress-to-fracture (CSF) and then in terms of scission kinetics as described by the thermally activated barrier to scission (TABS). The experimentally observed scission kinetics of the arms can be represented by the TABS model, but a description of the core scission appears to demand consideration of several possible conformations of the branched polymers.