Proof: Connected Graph of Order n Has at least n-1 Edges | Graph Theory
A connected graph of order n has at least n-1 edges, in other words - tree graphs are the minimally connected graphs. We'll be proving this result in today's graph theory lesson!
We'll be using a special type of contradiction proof called a proof by minimum counterexample. If we assume that there is a graph contradicting our claim, we can consider one such graph of minimum order, then we will show that this "minimum order counterexample" is actually not a minimum order counterexample, producing a contradiction and proving our claim.
Connected graphs with one less edge than vertices NEVER have cycles, and connected graphs with no cycles are called tree graphs; check out these lesson on them...
Intro to Tree Graphs: • Intro to Tree Graphs | Trees in Graph...
Proof that a tree graph of order n has size n-1: • Proof: Tree Graph of Order n Has Size...
Proof that a connected graph with n vertices and n-1 edges is a tree graph: • Proof: Graph with n Vertices and n-1 ...
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