Prove that if $G$ is a simple graph on n vertices such that $\delta(G) \geq \lfloor n/2\rfloor$, then $G$ is connected.
116932
Proving a simple graph is a connected graph
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
90256
Example of a simple graph isomorphic to a permutation group.
1453
Prove that the graph is connected
55944
Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
87760
Determine the diameter of a graph of order $n \geq 3$ where $\delta (G) \geq \frac{n-1}{2}$.
19807
Connected graph with colored edges
123742
Proving connectedness of the $n$-sphere
17470
Does path-connected imply simple path-connected?
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
31854
Proof - raising adjacency matrix to $n$-th power gives $n$-length walks between two vertices
127277
Graph Theory: Tree has at least 2 vertices of degree 1
49879
A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
4112
How to prove that a simple graph having 11 or more vertices or its complement is not planar?
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.