Unit I
Theorem 1
G is connected iff it's vertex set can be partitioned into two sets such that no edge has its one end in V1 and other end in V2.
Theorem. 2
if a graph has exactly two vertices of odd degree then there exists a path between those two vertices
theorem 3
If a connected graph G has n vertices and k components the. it has atmost (n-k)(n-k+1)/2 edges
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