How many vertices in this tree have degree 1.
118938
Number of leaves in a tree (all types of trees)
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?
117349
counting triangles in a graph or its complement
17086
The number of (non-equal) forests on the vertex set V = {1, 2, ...,n} that contains exactly 2 connected components is given by
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.
79040
Graph of $|x| + |y| = 1$
142103
find all self-complementary graphs on five vertices
138643
Prove that at most $2k+1$ independent sets form the set of vertices of a graph, where $k$ is the maximum degree.
63379
Enumerate non-isomorphic graphs on n vertices
13767
Number of nodes in binary tree given number of leaves
19413
Degree sequence multigraph without loop
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
157939
prove that a graph is one-ended
127701
How many distinct ways are there to $2$-color the $8$ vertices of a cube?
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
70252
Can a self-complementary graph on 100 vertices have precisely one vertex of degree 50?