(a)
Prove that if there is a walk from v to w, then there is a walk from v to w that has length less than or equal to n − 1.
Given information:
Let G be a graph with n vertices, and let v and w be distinct vertices of G.
Proof:
The adjacency matrix
A graph s connected if there exists a path between every pair of vertices.
G is a graph with n vertices
To proof: If there is a walk from v to w, then there is a walk from v to w that has length less than or equal to n − 1.
PROOF:
Let us assume that there exists a walk W from v to w and let the length of this walk be m.
If
(b)
Prove that G is connected if, and only if, every entry of