Show that each vertex $v$ of a tree $T$ appears $\deg(v)-1$ times in Prüfer sequence of $T$.
113305
Proof using Prüfer encoding
4240
The proof of Triple Vector Products
21807
on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
91896
Induction (Geometric sequence)
46309
Prove that this graph is nonplanar
80670
'Lines' in the Euler phi graph
65168
Proof of sequence inequality
50525
Prove that $(n, n, n-1, n-1, \ldots , 4, 4, 3, 3, 2, 2, 1, 1)$ is a graphic!
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
86826
Almost a Vandermonde matrix
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
53924
What is the smallest $n$ for which loopless graphs contain non-isomorphic $n$-vertex graphs with the same degree sequence?
20581
How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
110167
A conjecture with connection to the $abc$-conjecture
127277
Graph Theory: Tree has at least 2 vertices of degree 1
146933
Proving bipartition in a connected planar graph
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$