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I need help with a graph theory questionb) Let T be a tree with more then one vertex,...

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ashifs | Student, Undergraduate | Honors

Posted November 9, 2011 at 2:31 AM via web

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I need help with a graph theory question

b) Let T be a tree with more then one vertex, prove that T must
have atleast one vertex of degree 1

Tagged with graph theory, math

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted November 10, 2011 at 11:54 AM (Answer #1)

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A tree is an acyclic, connected graph. If the graph has more than one vertex, and every vertex has at least degree two, then there must be a cycle which contradicts the given that the graph is a tree.

Any vertex of degree at least 2 is a cut vertex, and any nontrivial graph contains at least two vertices that are not cut vertices.

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