Show that a graph has a unique MST if all edges have distinct weights
113902
Show that there's a unique minimum spanning tree if all edges have different costs
26251
Prove self-complementarity of regular graph with given order.
145194
Matrix graph and irreducibility
119543
Counting edges in a specially defined graph
15651
How to add a list of vectors (lists) to a directed graph as an edge weight?
75101
Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices...
102539
Min. number of vertices in graph as function of $\kappa(G)$ and $\operatorname{diam}(G)$
86271
Spanning Trees: Prove if $e_1$ is an edge in $X$ that isn't in $Y$, then there exists an edge ...
7626
Proving that every connected graph has a vertex whose removal will not disconnect the graph.
23008
For all $1 \leq i < j \leq k$, the subtrees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$.
27373
Graph Proof by induction.
34099
Proving that the empty set is unique
71154
Why a complete graph has $\frac{n(n-1)}{2}$ edges?
72417
Bipartite graphs
78243
graph-theory problem about outdegree and indegree
37754
Number of vertices of a complete graph with $n$ edges
146933
Proving bipartition in a connected planar graph