Minimum number of cycles in a connected graph.
29467
Prove that the minimum number of cycles is $m-n+1$
37754
Number of vertices of a complete graph with $n$ edges
100978
If a graph with $n$ vertices and $n$ edges there must a cycle?
83872
Isomorphisms for graphs with loops and multiple edges
91229
Complexity of counting the number of triangles of a graph
158856
Prove that a graph with the same number of edges and vertices contains one cycle
44563
Weakly Connected Graphs
121402
Planar Realization of a Graph in Three-Space
71170
Upper Bound on the Chromatic Number of a Graph with No Two Disjoint Odd Cycles
100168
Prove the existence of a graph of 15 vertices with some vertices degree given
138226
Finding All n-regular graphs on m vertices
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
1453
Prove that the graph is connected
45448
Minimum number of $k$-partitions of a set of size $n$ to enumerate all $n \choose k$ combinations
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
70761
Number of ways to connect sets of $k$ dots in a perfect $n$-gon
6429
prove that a connected graph with $n$ vertices has at least $n-1$ edges