Given a complete graph of $n$ vertices $K_n$ (has all possible edges – one edge between pair of vertices).
71154
Why a complete graph has $\frac{n(n-1)}{2}$ edges?
99806
Given an undirected Graph
27407
every planar graph can be expressed as a union of five edge-disjoint forests
149538
graph theory - clique graph
68638
Show that if $n\geq 3$, the complete graph on $n$ vertices $K_n$ contains a Hamiltonian cycle.
138465
Graph Coloring and Complete Graph
67887
Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges
38466
Proving that the number of vertices of odd degree in any graph G is even
17086
The number of (non-equal) forests on the vertex set V = {1, 2, ...,n} that contains exactly 2 connected components is given by
72417
Bipartite graphs
158083
If $G$ is a connected graph with $n$ vertices and $n - 1$ edges then $G$ is a tree, using Induction.
33316
Show that if $G$ is simple a graph with $n$ vertices and 􏰈the number of edges $m>\binom{n-1}{2}$, then $G$ is connected.
100466
The number of labelled graphs with all vertices of even degree
28877
Graph with $k$ components.
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
89531
Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
3786
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$