G is a graph with 100 vertices and $G \cong \overline{G}$. Is it possible that there is ONLY 1 vertex of valency 50 in G?
70252
Can a self-complementary graph on 100 vertices have precisely one vertex of degree 50?
10930
Why is the Petersen graph no Cayley graph?
7062
Can the complete graph $K_9$, be 2-coloured with no blue $K_4$ or red triangles?
17868
How to calculate the number of possible connected simple graphs with $n$ labelled vertices
4112
How to prove that a simple graph having 11 or more vertices or its complement is not planar?
142917
Graph vertex chromatic number in a union of 2 sub-graphs
61340
Prove that there exists bipartite graph with this degree sequence: $(3,3,3,3,3,5,6,6,6,6,6,6,6,6)$
129752
How to find whether it is possible for each vertex of a graph to have a different degree?
140471
Is $ G \cong G/N \times N$?
9847
Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
100289
Question about self-complementary graphs
138226
Finding All n-regular graphs on m vertices
79730
$G$ is a planar, connected graph. Let $n$ be number of vertices, $m$ number of edges and $f$ number of faces. Prove that dual graph $G*$ has $f(G*)=n$
91134
In any finite graph with at least two vertices, there must be two vertices with the same degree
126060
Proving that a Euler Circuit has a even degree for every vertex
25002
Is this true: any bipartite graph with unbalanced vertex parity is not Hamiltonian?
119304
Latin Square and Graph Theory