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.

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...

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 …

Oct 7, 2017 · $P \implies Q$, we want to show that if a connected graph $G$ has an Euler circuit, then all $v \in V (G)$ have even degree. An Euler circuit is a closed walk such that every edge in a …

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:

0 IF it is a simple, connected graph, then for the set of vertices {v: v exists in V}, v is adjacent to every other vertex in V. This type of graph is denoted Kn. For Kn, there will be n vertices and (n (n-1))/2 …

May 30, 2015 · What are the conditions for the complement of a connected graph to be connected? In particular, when is the complement of a connected regular graph connected? I feel that if the …

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, …