hw3 - 22.2 a) 1) The root of r is an articulation point of...

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Unformatted text preview: 22.2 a) 1) The root of r is an articulation point of G The root of G has at least two children .- let r be the root of G . If r has no child, the G has only one vertex r . Thus r is not articulation point of G according to definition. If r has one child, all the vertices of G can be reachable through the child of r . Since G is still connected graph even if r is removed from G. Thus r is not articulation point of G. 2) The root of G has at least two children The root of G is an articulation point of G.- Assume the root r of G has two child c1 and c2 and r is not articulation point of G. Then there is a path between c1 and c2 which does not include r , and we can reach c2 through c1. This means c2 is a sub-child node of c1, and it is contradict to our assumption that c1 and c2 are both children of r . Thus r is an articulation point of G. b) 1) v is an articulation point of G v has a child s such that there is no back edge from s or and descendant of s to a proper ancestor of v....
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hw3 - 22.2 a) 1) The root of r is an articulation point of...

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