Consider N switches supporting ‘k’ VLAN groups that are connected via a trunking protocol.
• Each switch has two trunking ports. One is input port and another one is output port.
• The first switch does not use input port. It uses only output port. Therefore, the number of ports required by the first switch is 1.
• The last switch does not use output port. It uses only input port. Therefore, the number of ports used by last switch is 1.
• The remaining N-2 switches other than the last switches use 2 ports each. Therefore, the number of ports all these switches uses is 2 x (N - 2) ports.
• The total number of ports that are used by all these N switches is
2 + 2 x (N - 2) = (2 x N) - 2 ports.
Therefore, (2 x N) - 2 ports are required to connect the switches.
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