Is there any command to check that how many switches are connected to a switchport, downstream... Like 1st switch is connected to 2nd and 2nd is connected to 3rd, can we check all down stream device by logging in to 1st switch..?
no there is not a similar command because the switches act as transparent bridge.
To discover the topology you need to go to connect to swich 2 and then to switch 3
You can use
show cdp neighbors
and show spanning-tree
to help you understand and draw the topology
Hope to help
Giuseppe
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