Utilizing the inherent sparsity of massive multiple-input multiple-output (MIMO) channels in the beam domain, we propose a bipartite graph approach for frequency-division duplexing (FDD) vehicle-to-vehicle (V2V) underlay massive MIMO transmission. First, the physically motivated constraints are introduced to schedule the users with channel dimension no larger than the pilot dimension and beam directions with strong channel power as well as weak interference. We then develop an optimization problem which is formulated as a mixed-integer linear program (MILP) to maximize the rank of the effective channel matrix subject to the introduced constraints. We further provide a channel estimation and precoding scheme for the base station and each V2V transmitter over the equivalent reduced-dimensional channels based on the solution of MILP. Numerical results show the superiority of the proposed bipartite graph approach in terms of pilot overhead and spectral efficiency over the conventional baseline.