Math Problem Statement
Prove: If G is a connected graph with n vertices and (n-1)edges, then G is a tree. (Hint: think about the spanning tree of G )
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Graph Theory
Trees
Spanning Trees
Formulas
Number of edges in a tree = n - 1 (for n vertices)
Theorems
Properties of Trees
Spanning Tree Theorem
Suitable Grade Level
Undergraduate Level
Related Recommendation
Prove Tree Edge Formula and Characterize Connected Graphs as Trees
Graph Theory: Proving Edges in a Connected Graph with No Separation
Proof that in a Tree with 2n Vertices, You Can Choose n Vertices with No Edges Between Them
Prove Existence of Disconnected Graph with (n-1)(n-2)/2 Edges for n ≥ 2
Proof: Acyclic Graph with n Vertices and n - 3 Components Has Specific Leaf Counts