An undirected graph is connected when there is a path between every pair of vertices. In a connected graph, there are no unreachable vertices. A graph that is not connected is disconnected. An …

Dec 18, 2014 · In your example, it is not a directed graph and so ought not get the label of "strongly" or "weakly" connected, but it is an example of a connected graph. As soon as you make your example …

Oct 29, 2014 · 1 By contradiction: suppose the graph is not connected, then it has at the very least $2$ connected components, so the size of the smallest component is at most $\frac {n} {2}$ Meaning the …

Jul 24, 2020 · Weakly connected means that if you replace all the directed edges with undirected edges then the resulting undirected graph is connected. Semiconnected implies weakly connected.

Feb 28, 2023 · The examples used in the textbook show a visualization of a graph and say "observe that G is connected" or "notice that G is connected". Is there a method to determine if a graph is …

Here's alternative proof that a connected graph with n vertices and n-1 edges must be a tree modified from yours but without having to rely on the first derivation:

A connected graph is a graph with no disjoint subgraphs. A simple graph is a graph with no loops or multiple edges. Easy Question: What are the necessary and sufficient conditions on the order (n...

0 It is correct to say that a connected graph is only when there exist some vertex that is connected to all other vertices? I think this is correct, because a connected graph not all vertices are connected …

More explanation: The adjacency matrix of a disconnected graph will be block diagonal. Then think about its complement, if two vertices were in different connected component in the original graph, …

Apr 20, 2017 · You can prove it with induction. For 1 and 2 vertices it is trivial. Then if you add a new vertice to the graph, you have to connect this vertice to the rest, to make the graph connected. Thus, …