A circuit-free graph has ten vertices and nine edges. Is it connected? Why?
Whether a circuit free graph, having ten vertices and nine edges, is connected or not.
Any tree with vertices has
Suppose is a circuit free graph with ten vertices and nine edges.
Let be the connected components of .
To show that is connected, we will show that .
Each is a tree since each has vertices.
Note that since has ten vertices in all,
Since for any positive integer , any tree with vertices has edges, we have edges, edges,
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