Oct 14, 2023 · Now, let's use these properties to prove the statement. If a graph has an Eulerian path, there must be exactly two vertices with odd degrees (the starting and ending vertices) and all other …

Usually one speaks of adjacent vertices, but of incident edges. Two vertices are called adjacent if they are connected by an edge. Two edges are called incident, if they share a vertex. Also, a vertex and …

Dec 27, 2025 · The above construction provides an explicit example of a $6$ -regular graph on $19$ vertices that is locally a $ (3,3)$ -windmill. If one wishes to analyze the graph by hand (for example, …

Dec 6, 2025 · The least number of vertices that a polyhedron can have, such that its diagonal faces enclose an interior solid region? Note: "interior" means the solid does not intersect the polyhedron …

Here's an alternative proof that a connected graph with n vertices and $n-1$ edges must be a tree, modified from yours, but without having to rely on the first derivation:

Nov 8, 2023 · My question is, what is an ordering of a simplex? Is it just a permutation of the vertices or does it have to satisfy some other rules? If it's defined to be a permutation of vertices, then we draw …

Oct 23, 2022 · I would approach the issue from a completely different direction. Consider a triangle in 3D with vertices at $\vec {v}_0$, $\vec {v}_1$, and $\vec {v}_2$. It has a directed normal $\vec {n}$, …

Jan 23, 2015 · To prove that the number of odd vertices in a simple graph is always even, we can use the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is twice …

Dec 11, 2010 · Anyone know of an online tool available for making graphs (as in graph theory - consisting of edges and vertices)? I have about 36 vertices and even more edges that I wish to draw. …

If you have a hollow triangular mesh and you put a marble inside of it, will not the marble go to any of the vertices? Yes it will. Why? Because the altitude is the lowest there of all points inside of the mesh. …