Show that the number of spanning trees of the complete graph $K_n$ is $n^{n−2}$
65574
How to prove that total number of non-isomorphic labelled trees of order $n$ is $n^{n-2}$?
146933
Proving bipartition in a connected planar graph
38466
Proving that the number of vertices of odd degree in any graph G is even
8458
Combinatorics problem based on Ferrers graph
44013
How many trees over ${1,2,3,...n}$ with conditions
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.
7062
Can the complete graph $K_9$, be 2-coloured with no blue $K_4$ or red triangles?
71154
Why a complete graph has $\frac{n(n-1)}{2}$ edges?
117349
counting triangles in a graph or its complement
154564
Prove that the sum of minimum edge cover and maximum matching is the vertex count
49045
Graph theory: Tree holds two sub-tree with an amount of vertices
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
150156
Proving that $S_n$ has order $n!$
29467
Prove that the minimum number of cycles is $m-n+1$
28877
Graph with $k$ components.
145718
Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
13226
If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree?