Let $n \geq 4$. How many labeled trees are there with $n$ vertices where vertex with label 1 has degree 3?
44304
Number of labeled trees which have one vertex of degree 4
158856
Prove that a graph with the same number of edges and vertices contains one cycle
6429
prove that a connected graph with $n$ vertices has at least $n-1$ 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?
108631
Calulating the Ramsey number $R(T, K_{1,n})$ of a tree $T$ and bipartite graph $K_{1,n}$
106801
Labelled spanning trees of $K_n-e$
145718
Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
57221
counting the number of elements in a conjugacy class of $S_n$
91253
Proving that every graph that each vertex at degree 2 must contain a cycle
65574
How to prove that total number of non-isomorphic labelled trees of order $n$ is $n^{n-2}$?
98991
How many different spanning trees of $K_n \setminus e$ are there?
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
90747
Upper bound on $\chi(G)$ for a triangle-free graph
68638
Show that if $n\geq 3$, the complete graph on $n$ vertices $K_n$ contains a Hamiltonian cycle.
55944
Chromatic polynomial of connected graph $ \leq x(x-1)^{n-1}$
100168
Prove the existence of a graph of 15 vertices with some vertices degree given