Computer Information Systems

Step 1: Understanding the Properties of a Connected Graph Minimum Number of Edges: In a connected graph with ∣ V ∣ |V| ∣ V ∣ vertices, there must be at least ∣ V ∣ − 1 |V| - 1 ∣ V ∣ − 1 edges. This is because a tree, which is a minimal connected graph, has exactly ∣ V ∣ − 1 |V| - 1 ∣ V ∣ − 1 edges. Maximum Number of Edges: In a connected simple graph with ∣ V ∣ |V| ∣ V ∣ vertices, the maximum number of edges is ( ∣ V ∣ 2 ) \binom{|V|}{2} ( 2 ∣ V ∣ ) , which represents a complete graph K ∣ V ∣ K_{|V|} K ∣ V ∣ . This is given by: <s

Computer science

Prove that if a graph G = (V,E) is connected, then log |E| = BigO(log |V|).

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Computer science

Computer science

Manu

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