The operating system kernel manages system resources and makes them available to user-space programs through system calls (syscalls). Vulnerabilities in this syscall handling code could allow user-space programs to exploit the kernel, leading to information leaks or privilege escalation. Finding and patching kernel bugs is therefore critical for system security. Coverage-guided kernel fuzzers such as Syzkaller have proven to be quite effective at discovering kernel bugs through mutation and generation of syscall sequences. Recent fuzzers have integrated techniques for learning dependency relations between syscalls in order to increase the efficacy of fuzzing. Our tool, SyzGrapher, extends this vein of research, aiming to capture the semantics of syscalls to construct test cases that reach deep, interesting code. We focus specifically on improving handling of kernel resources, such as file descriptors and sockets. We design and implement an analysis to learn fine-grained, resource-based dependencies between syscalls and integrate these learned dependencies into a fork of Syzkaller with resource-centric, graph-based mutations. Our evaluation demonstrates that SyzGrapher achieves more code coverage and finds more bugs than state-of-the-art tools. Additionally, in a 7-day fuzz campaign, SyzGrapher found 38 new vulnerabilities across 4 versions of the Linux kernel, 16 within the first day of fuzzing.