The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is _________.

To determine the maximum number of IPv4 addresses that can be accommodated in the Record Route (RR) option:

1. Maximum IPv4 Header Size: The Internet Header Length (IHL) field in the IPv4 header is 4 bits, representing the header length in 32-bit (4-byte) words. The maximum value of IHL is $15$, which corresponds to a maximum header size of:

   $$15 \times 4 = 60\text{ bytes}$$

2. Base Header Size: The standard base header (without options) is $20\text{ bytes}$.

3. Maximum Options Field Size:

   $$\text{Max Options Size} = 60 - 20 = 40\text{ bytes}$$

4. Overhead of the Record Route Option: The Record Route option has a 3-byte overhead:

   • Option Type / Code: 1 byte (value $7$)

   • Option Length: 1 byte

   • Pointer: 1 byte

5. Space Available for IPv4 Addresses:

   $$\text{Available space} = 40 - 3 = 37\text{ bytes}$$

6. Maximum Number of IPv4 Addresses: Since each IPv4 address occupies 4 bytes:

   $$\left\lfloor \frac{37}{4} \right\rfloor = 9\text{ addresses}$$

   Total option size used $= 3 + (9 \times 4) = 39\text{ bytes}$ (plus 1 byte of NOP / padding to align to a 4-byte boundary).

Therefore, the maximum number of IPv4 router addresses that can be listed is 9 [20.0].