I am studying graph thoery and come up with a thought that,
if $G$ is acyclic graph with degree of every vertex is at least two then $G$ is connected!
The graph is said to be disconnected if at least two vertices of the graph are not connected by a path, otherwise it's said to be connected.
Is this true! if it is then how can I prove that?
All I can imagine is infinite graph which is tree.
(Degree of vertex of graph is number of vertices adjacent to that vertex and acyclic means graph without cycle).
A finite graph in which every vertex has degree $\geq2$ has a cycle, so the statement is vacuously true. In the infinite, the statement is false, since a forest of two infinite trees is a counterexample.