Repeat Problem below, if the distance is changed to 8 hops.
If the destination node is located at 5 hops apart from a given
source node, what is the maximum possible value of
(a) The number of alternate paths of length of 5 hops?
(b) Alternate disjoint paths of length 5 hops?
(a) Alternate paths means a source node S can take A-B-C to destination D, it
also can take M-L-N to destination D if the formal link fails. If the destination
node is located at 5 hops apart from a given source node, every node is connected to exactly 4 adjacent node, therefore, source can connect with four adjacent node, among these four adjacent nodes, every node mostly can connect with another 3 nodes, then from 4 nodes arrive to destination. Therefore, there would be 4 x3x 3x1x1 = 36 alternate paths (maximum).
(b) For disjointness, no intermediate node should be common among the paths.
One simple way is to have a unique path between 12 nodes after 2 links from
either source or destination, giving 4x3x1x4 = 48 disjoint paths (maximum).
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