Prove that $G$ graph contains prime cycle, which length is not less than $\delta(G) + 1$
101520
Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
11329
Proving a graph has no Hamiltonian cycle
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.
1453
Prove that the graph is connected
31347
$A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?
28877
Graph with $k$ components.
85541
What is the maximum length of a circuit in the complete graph on n vertices.
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
108417
Cycles of length k in a complete simple graph with n vertices
87760
Determine the diameter of a graph of order $n \geq 3$ where $\delta (G) \geq \frac{n-1}{2}$.
89452
Proof about Graph with no triangle
31854
Proof - raising adjacency matrix to $n$-th power gives $n$-length walks between two vertices
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?
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.