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 …

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 …

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} …

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 …

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 …

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:

Question: Consider a simple graph G with n vertices. What is the minimum number of edges that G must have in order to ensure that it is connected? Justify your answer. My attempt: Let G = …

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 …

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 …

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 …