Were you executing the arp command on your Fedora box or on the router? It's not obvious by your post.
You will need to run the arp command on your router to see the arp cache for the router.
Running the arp command on your Fedora box will show only those devices communicating with your Fedora box (printers, etc.).
If the command takes too long to complete you can use "arp -n" to avoid resolving IP addresses to names.
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