In multi-cell non-orthogonal multiple access (NOMA) systems, designing an appropriate user grouping strategy is an open problem due to diverse quality of service (QoS) requirements and inter-cell interference. In this paper, we exploit both game theory and graph theory to study QoS-aware user grouping strategies, aiming at minimizing power consumption in downlink multi-cell NOMA systems. Under different QoS requirements, we derive the optimal successive interference cancellation (SIC) decoding order with inter-cell interference, which is different from existing SIC decoding order of increasing channel gains, and obtain the corresponding power allocation strategy. Based on this, the exact potential game model of the user grouping strategies adopted by multiple cells is formulated. We prove that, in this game, the problem for each player to find a grouping strategy can be converted into the problem of searching for specific negative loops in the graph composed of users. Bellman-Ford algorithm is expanded to find these negative loops. Furthermore, we design a greedy based suboptimal strategy to approach the optimal solution with polynomial time. Extensive simulations confirm the effectiveness of grouping users with consideration of QoS and inter-cell interference, and show that the proposed strategies can considerably reduce total power consumption comparing with reference strategies.