So, I have this graph and it is asked whether this graph is a spanning tree or not. According to me this is not a spanning tree because there is no path from, say node 1 to node 2, for instance. That is, according to me, a spanning tree must have path to every node from a starting node. In short, I just want to know if this is a spanning tree or not and if my reasoning is correct or not.
Thanks in advance.
On
Trees are, by definition, connected graphs. When you consider $G$ with $V = \{1, 2, ..., 9\}$, you can see it is not connected, so $G$ isn't even a tree. If you consider $G_1$ with $V = \{1, 2, 3\}$, $G_2$ with $V = \{4, 5, 6\}$ and $G_3$ with $V = \{7, 8, 9\}$, however, these are graphs with spanning trees.
In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree. The Wikipedia article on spanning trees is very elucidating.
No, it's not a spanning tree. These graphs are disjoint so they are not a tree, let alone a spanning tree.