This study examined viscoeslastic properties of two flexible dumbbell-shaped polystyrene (PS) samples, D-30/120/30 and D-30/240/30, which possess the same ring size (M-R similar to 30 kg/mol) and different lengths of central linear chains (M-L similar to 120 and 240 kg/mol) in bulk and solution. In bulk, both dumbbell PS samples exhibited an extremely long entanglement plateau in dynamic oscillatory measurements, and their terminal relaxation behavior was not observed in our experimental window. In stress relaxation measurements, dumbbell samples in bulk exhibited considerably slower terminal relaxation than high-molecular-weight linear PS samples (M similar to 10(6) g/mol), and a clear difference between two dumbbell PS samples was observed in the long time regime, i.e., terminal relaxation of D-30/240/30 is much slower than that of D-30/120/30. These results suggest that (i) the dumbbell polymer forms a characteristic "network" where two rings on both ends in a molecule spontaneously thread the ring part of other dumbbell chains and (ii) this type of interchain interaction resulting in network formation becomes more dominant than usual entanglements similar to linear chains. The network of dumbbell chains starts to relax their stress when the intermolecular threading is released, and this release process tends to occur more frequently for the dumbbell with a shorter central chain, D-30/120/30, than that with a longer one, D-30/240/30. In dioctyl phthalate (DOP) solutions of D-30/240/30, where DOP is known as a theta-solvent for PS at 22 degrees C, in a relatively high concentration regime (i.e., 20-30 wt %), the solutions exhibited an entanglement plateau and higher viscosity than the corresponding linear PS solutions, suggesting that the characteristic entanglement originating from intermolecular threading of dumbbell chains is still dominant in the solution. On the contrary, in a lower-concentration regime (<= 8 wt %), the D-30/240/30 solutions exhibited similar viscosities to the linear PS ones, wherein the dumbbell molecules behave like unentangled/isolated chains.