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When adjusting Maximum Transmission Unit (MTU) sizes, the potential for packet fragmentation is a critical factor to consider. Fragmentation occurs when packets exceed the MTU size allowed on a network segment. If a packet is larger than the allowed MTU, it must be broken down into smaller packets, which can lead to performance issues, increased latency, and potential packet loss.

Choosing an appropriate MTU size can help optimize network performance by avoiding fragmentation, ensuring that packets can be transmitted without the need for division. This is particularly important in environments where timely and efficient data transfer is essential. Additionally, keeping an eye on MTU sizes can help reduce the processing load on routers and switches, as they won't need to reassemble fragmented packets.

While network speed, the number of connected devices, and the type of routing protocol used can influence network performance, they are not as directly related to the operational implications of MTU adjustments as the potential for packet fragmentation. High network speeds with an inadequately set MTU may still lead to fragmentation issues, which essentially affects data integrity and transmission efficiency.