Induction proof that the number of edges of a complete graph with $x$ vertices is always $\frac{x^2-x}{2}$
122998
number of edges induction proof
49879
A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
150508
∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
6165
Proof by Induction $n^2+n$ is even
49703
Analogue of closed graph theorem
48184
Prove a graph Containing $2k$ odd vertices contains $k$ distinct trails
37466
Questions on "All Horse are the Same Color" Proof by Complete Induction
145181
How can I prove the maximum number of edges?
59831
How to relate combinatorial proof to bipartite graphs?
49585
Proof a graph is bipartite if and only if it contains no odd cycles
22073
Prove by induction that $n^2<n!$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
158856
Prove that a graph with the same number of edges and vertices contains one cycle
89452
Proof about Graph with no triangle
79040
Graph of $|x| + |y| = 1$
33786
Proof that a certain fraction is always an integer