In OSPF, the election of the designated router (DR) and backup designated router (BDR) is based on the OSPF network type. The network types include:
Broadcast: This is the default network type for Ethernet interfaces. In a broadcast network, OSPF elects a DR and BDR. All other routers become DROTHERs. To prevent the election of a DR/BDR, you can configure the interface as non-broadcast (NBMA) using the ip ospf network non-broadcast command.
Point-to-Point: This network type is used for point-to-point links (e.g., serial links). There is no DR/BDR election in point-to-point networks.
Point-to-Multipoint: This network type is used for point-to-multipoint links (e.g., Frame Relay). There is no DR/BDR election in point-to-multipoint networks.
Point-to-Multipoint Non-Broadcast: Similar to point-to-multipoint, but explicitly configured as non-broadcast. There is no DR/BDR election in point-to-multipoint non-broadcast networks.
Loopback: Loopback interfaces are always treated as point-to-point.
Virtual-Link: Used for OSPF virtual links.
Sham-Link: Used for OSPF sham links.
Demand Circuit: Used for demand circuits (e.g., ISDN).
Non-Broadcast: Explicitly configured as non-broadcast. There is no DR/BDR election in non-broadcast networks.
Reference:
Implementing and Operating Cisco Service Provider Network Core Technologies (SPCOR) v1.0 Cisco Learning Network Store - SPCOR Training

The error message "%CLNS-4-AUTH_FAIL: ISIS: LAN LIIH authentication failed" indicates that there is an authentication failure in the IS-IS routing protocol between routers R1 and R2. In the exhibit, it can be observed that R2 has a state of "UP" for its IS-IS neighbor relationship, while R1 is in "INIT" state. This discrepancy in states indicates an issue with the establishment of the neighbor relationship, which can be attributed to an authentication failure at both Level 1 and Level 2 PDUs as indicated by option B.