The definition of a connected graph states that: A graph G G is called connected provided for each pair a,b a, b with a≠ b a ≠ b of vertices ∃ ∃ a walk joining a and b. (equivalently a chain joining a a and b …

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:

Let $G$ be a $k$ -connected graph. Meaning, $G$ has no fewer than $k$ vertices, and for every set of $k-1$ or fewer vertices, if we remove them from $G$, the graph stays connected (Of course, $G$ …

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, …

Apr 28, 2017 · What do you think is the most efficient algorithm for checking whether a graph represented by an adjacency matrix is connected? In my case I'm also given the weights of each …