ospf : Number of adj of DR and BDR in a broadcast media

CCIE_2011

Morning all ....

I have red every where that the number of adj created with the DR is n-1 (assuming there is no BDR elected all routers are config with priority 0 expect DR, n=number of routers). which is correct

therefore:
(num of routers, num.adj)
(1,0)
(2,1)
(3,2)
(n, n-1)

now if we introduce a new router and it's priority is 1. it will be elected as BDR and it will form adj with all routers in the broadcast domain.
therefore BDR will form n-1 adj with all routers (n now includes BDR).
therefore total num of adj = n-1 of DR + n-1 of BDR = 2n-2

i have red everywhere that the formula is 2n-1. which really confused me.

Please some one to explain where is my misunderstanding.
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NeonNoodle

With a DR and BDR on a network consisting of n (>=2) routers, there are 2n-3 adjacencies. There are n-2 DROthers. They form an adjacency with both the DR and the BDR. That gives us (n-2)+(n-2) = 2n-4 adjacencies. But there is also an adjacency between the DR and BDR. So that means we have 2n-4+1 = 2n-3 adjacencies.

The answer is not 2(n-1)=2n-2 because you've counted the adjacency between the DR and the BDR twice. So you have to subtract 1 from 2n-2, which gives you 2n-2-1=2n-3 again.

CCIE_2011

thanks alot now it is clear