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 …

Jul 24, 2020 · Weakly connected: if, and only if, the graph is connected when the direction of the edge between nodes is ignored. As far as I can tell, these definitions are identical.

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 …

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...

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 …

This result is immediate by induction once you have established (as lemma) that in every connected graph with at least two vertices there are at least two vertices that can be individually removed (with …

I think this is correct, because a connected graph not all vertices are connected together, but at least no vertex is not connected? Isn't that the above definition is saying?

What am I missing in here? Connected question: A connected k-regular bipartite graph is 2-connected. Edit: To clarify, my definition of graph allows multiple edges and loops. If a graph has none of these, …