How to prove that at least two vertices have the same degree in any graph?
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?
49193
Constructing a graph from a degree sequence
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
115085
number of vertices in a self-complemntary graph
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
116932
Proving a simple graph is a connected graph
121130
Graph with even vertices and ${n-1}\choose 2$ $+ 1$ edges has a perfect matching
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
33603
How to get all Perfect or Near-Perfect Matchings of a graph
117685
Prove that a bipartite planar graph has a vertex of degree at most 3
138226
Finding All n-regular graphs on m vertices
72417
Bipartite graphs
79631
Find a graph on eight vertices with a pair of pseudosimilar vertices
31626
proving that a graph is hamiltonian (Ore's theorem)
37754
Number of vertices of a complete graph with $n$ edges
45193
prove or supply counter example about graph
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.