The memristors in binary metal oxide structures have attracted attentions since the current nonvolatile memory (NVM) has been approaching the scaling limit. Memristors having excellent scalability, high speed, and low power operation, is desired for current hardware needs and future artificial intelligence in-memory computational hardware platform. In high-density cross-bar array architecture, selector devices are essential to suppress the sneak path current and to avoid the reading errors. Despite that the additional selector device has commonly been proposed one selector-one resistor (1S1R) design for array applications, it rises the process complexity and cost. In this work, selectorless lR-only graphite-based memristor devices have been demonstrated by utilizing the nonlinear (NL) resistive switching (RS) characteristics with SET compliance and gap design method for memristor array applications.