Is a Star Graph with Infinite Rays Considered an Infinite Tree?

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A star graph with infinite rays is not considered an infinite tree because it lacks the branching structure characteristic of trees. According to Konig's Lemma, every infinite tree contains an infinite path, which is not applicable to a star graph since it has a single central point connected to infinite rays without further branching. The discussion highlights the distinction between the structure of a star graph and that of an infinite tree. The central point in a star graph does not create the necessary complexity to qualify as an infinite tree. Therefore, while both structures are infinite, their definitions and properties differ significantly.
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"Konig's Lemma" essentially says that every infinite tree contains an infinite path.

I didn't know that myself until I read your question, went to "google.com" and entered "Konig's Lemma". I recommend you try that yourself.
 
What about the tree which consists of a central point, x, with infinite points around it connected only to x?

Why is this not counted as an infinite tree?
 

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