Maximum number of IPv4 router addresses in the record route (RR) option field of an IPv4 header is 9

Explanation:

The record route (RR) option field is an optional field in the IPv4 header that allows a packet to carry a list of router addresses that the packet has traversed. This option is useful for debugging purposes and for network analysis.

IPv4 Header Structure:
- Version (4 bits): Specifies the version of the IP protocol being used.
- IHL (4 bits): Specifies the length of the IP header in 32-bit words.
- Type of Service (8 bits): Specifies the type of service, such as priority or reliability.
- Total Length (16 bits): Specifies the total length of the IP packet, including the header and data.
- Identification (16 bits): Used for uniquely identifying IP fragments.
- Flags (3 bits): Used for indicating fragmentation and reassembly.
- Fragment Offset (13 bits): Specifies the position of the fragment in the original IP packet.
- Time to Live (8 bits): Specifies the maximum number of hops the packet can take before it is discarded.
- Protocol (8 bits): Specifies the protocol used in the data portion of the IP packet.
- Header Checksum (16 bits): Used for error detection in the IP header.
- Source IP Address (32 bits): Specifies the source IP address of the packet.
- Destination IP Address (32 bits): Specifies the destination IP address of the packet.
- Options (variable length): Optional fields used for various purposes, such as record route, timestamp, etc.

Record Route (RR) Option:
The record route (RR) option is one of the optional fields in the IPv4 header. It allows a packet to carry a list of router addresses that the packet has traversed. This option is used for network analysis and debugging purposes.

Maximum Number of Router Addresses:
The RR option field has a limited length, and the maximum number of router addresses that can be listed in this field is 9. Each router address is 4 bytes long (32 bits), and the RR option field has a maximum length of 40 bytes. Therefore, the maximum number of router addresses that can be listed is 40 bytes / 4 bytes = 10 addresses.

However, one address slot is reserved for the source IP address, leaving only 9 slots available for router addresses. This means that a packet can carry a maximum of 9 router addresses in the RR option field.

Conclusion:
The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is 9. This is due to the limited length of the RR option field and one slot being reserved for the source IP address. The RR option field allows packets to carry a list of router addresses for network analysis and debugging purposes.