Proof that the chromatic polynomial of a simple graph G with n vertices has degree n.
57930
Chromatic polynomial properties
94838
Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
101520
Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
83036
f(g(x)) has a degree divisible by n
91253
Proving that every graph that each vertex at degree 2 must contain a cycle
126428
Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
110760
Chromatic Polynomial
90256
Example of a simple graph isomorphic to a permutation group.
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
139657
Prove that if $\chi(G-u-v)=\chi(G)-2$ for every vertices $u, v$ ($u \ne v$) then G is complete graph.
137322
Construction of a triangle-free graph of chromatic number $1526$
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.
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
28877
Graph with $k$ components.
110422
Prove that a graph $G$ is a forest if and only if every induced subgraph of $G$ contain a vertex of degree at most $1$
141983
Complex polynomial of degree $n$
38466
Proving that the number of vertices of odd degree in any graph G is even