A graph (G) is only connected as a topological if G is connected as a graph.
45805
(A question regarding:) the graph associated with an open cover of a topological space.
127919
prove that if $E$ is connected and $E \subseteq F \subseteq \overline{E}$, then $F$ is connected.
147961
Characterizing simply connected spaces
35458
Prove, that graph $G$ has at least $\chi(G)(\chi(G)-1)/2$ edges.
1453
Prove that the graph is connected
7665
If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.
78110
A connected k-regular bipartite graph is 2-connected.
79236
Topology on $\mathbb{R}$ strictly coarser (resp. finer) than the usual one which is still Hausdorff (resp. connected)
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
110422
Prove that a graph $G$ is a forest if and only if every induced subgraph of $G$ contain a vertex of degree at most $1$
113022
Is the graph $G_f=\{(x,f(x)) \in X \times Y\ : x \in X \}$ a closed subset of $X \times Y$?
46841
When is a graph isomorphic to the source?
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
132095
Motivation for the term "separable" in topology
126192
Connected, locally connected, path-connected but not locally path-connected subspace of the plane
131137
If ${\lvert{E(G)}\rvert}>{\lvert{V(G)}\rvert}+3$, graph $G$ has at least two disjoint cycles.
60746
Simply connected does not imply contractible. Is there a nice counter example in $R^2$?