Which encapsulation type is a Frame Relay encapsulation type that is supported by Cisco routers?

Cisco supports two Frame Relay encapsulation types: the Cisco encapsulation and the IETF Frame Relay encapsulation, which is in conformance with RFC 1490 and RFC 2427. The former is often used to connect two Cisco routers while the latter is used to connect a Cisco router to a non-Cisco router. You can test with your Cisco router when typing the command Router(config-if)#encapsulation frame-relay ? on a WAN link.

Note: Three LMI options are supported by Cisco routers are ansi, Cisco, and Q933a. They represent the ANSI Annex D, Cisco, and ITU Q933-A (Annex A) LMI types, respectively.

HDLC is a WAN protocol same as Frame-Relay and PPP so it is not a Frame Relay encapsulation type.