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Specialized graph data management systems have made significant advances in storing and analyzing graph-structured data. However, a large fraction of the data of interest still resides in relational database systems (RDBMS) due to their maturity and security reasons. Recent studies, in view of composability, show that the execution of graph queries over relational databases, (i.e., a graph layer on top of RDBMS), can provide competitive performance compared to specialized graph databases. While using the standard property graph model for graph querying, one of the main bottlenecks for efficient query processing, under memory constraints, is property projections, i.e., to project properties of nodes along paths matching a given pattern. This is because graph queries produce a large number of matching paths, resulting in a lot of requests to the data storage or a large memory footprint, to access their properties. In this paper, we propose a set of novel techniques exploiting the inherent structure of the graph (aka, a graph projection cache manager) to provide efficient property projections. The controlled memory footprint of our solution makes it practical in multi-tenant database deployments. The empirical results on a social graph show that our solution reduce the number of accesses to the data storage by more than an order of magnitude, resulting in graph queries being up to 3.1X faster than the baseline.