Let $n = 4k$ or $n = 4k+1$ for non-negative $k$. Prove that there exist a self-complementary graph $G = (V, E)$, where $|V| =n$
65639
Existence of a self-complementary graph
137691
What are the self-normalizing subgroups of $S_n$?
146386
Is there a reason why the number of non-isomorphic graphs with $v=4$ is odd?
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
129845
Prove that $T$ is a subgraph of $G$
48692
A problem about the graph theory
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
67926
$S_n$ is generated by elements of the form $(1k)$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
106801
Labelled spanning trees of $K_n-e$
69358
Given a simple graph and its complement, prove that either of them is always connected.
65744
How can I Prove that H=G or K=G
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles