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How to find a cut vertex in a graph?

 
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Eclipse IDE Windows XP Java
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currently I am on a data structure book called data structure and algorithms made easy in java, in that book(page 291), there is a discussion about finding cut vertexes in a given graph. but I have hard time to understand the concept. even I google about it and try to figure out. but not able to understand.. already I wasted 2 days on it... any body has idea about it? if yes, could you please explain?

Note: I understand the definition about cut vertex
 
Seetharaman Venkatasamy
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Yes!!! finally I have cracked it ... nice logic ;)
 
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