1.3 Tree Characterization Theorem (Proof:  ) Assume G is connected and |E| = |V| - 1 Prove that G is a tree… (by definition of a tree) –G is connected (trivial) –G does not have any circuits.
{"Image DocumentName": "1.3 Tree Characterization Theorem", "Image ImageDescription": "(Proof: \u00ac) Assume G is connected and |E| = |V| - 1. Prove that G is a tree\u2026 (by definition of a tree) G is connected (trivial) G does not have any circuits. Proof of (a): Trivial, since it\u2019s in the assumption. Before we prove (b), we need to prove another lemma. Lemma 2: Let G=(V,E) be a connected graph. Let C be a circuit in G. If an edge in C is removed from G to form G\u2019, then G\u2019 is still connected.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}