Why do graph degree sequences always have at least one number repeated?
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?
63379
Enumerate non-isomorphic graphs on n vertices
58103
number of permutations in which no two consecutive numbers are adjacent
71154
Why a complete graph has $\frac{n(n-1)}{2}$ edges?
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
157150
Is the maximum degree of a planar graph 5?
18383
List of ways to tell if degree sequence is impossible for a simple graph
138226
Finding All n-regular graphs on m vertices
15002
Unique (non-repeating) random numbers in O(1)?
65574
How to prove that total number of non-isomorphic labelled trees of order $n$ is $n^{n-2}$?
19250
Find a recurrence relation for the number of $n$-digit binary sequences with no pair of consecutive $1$s
78243
graph-theory problem about outdegree and indegree
158856
Prove that a graph with the same number of edges and vertices contains one cycle
17371
Recurrence relation for number of ternary strings that contain two consecutive zeros
156660
The set of all strictly increasing sequences of natural numbers
146386
Is there a reason why the number of non-isomorphic graphs with $v=4$ is odd?
99931
Number of connected graphs on labeled vertices, counted according to parity