Undirected: we can travel from point A and point B through an edge in both directions
Cannot have loops, so a vertex cannot have an edge to itself. Only connected to other vertices.
No multiple edges: only one edge between two vertices, cannot have multiple edges connecting the same pair of vertices.
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Not so sure I understand connectedness.
What does maximally connected mean?
Theorem 5 (Theorem 4.8.5 in the course notes). A graph G is disconnected if and only if there exists a non-empty proper subset of X of V (G) such that the cut induced by X is empty.
Basically saying that a graph has more than 1 component and if we make a nonempty cut X, there should be no edges induced. he Theorem states that a graph G is disconnected if and only if there exists a non-empty proper subset X of its vertex set V(G) such that the cut induced by X is empty, meaning that no edges cross between the vertices in X and the vertices in V(G) - X.