Proving that the number of vertices of odd degree in any graph G …
I'm having a bit of a trouble with the below question Given G is an undirected graph, the degree of a vertex v, denoted by deg(v), in graph G is the number of neighbors of v. Prove that the …
Graph theory: adjacency vs incident - Mathematics Stack Exchange
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 …
polyhedra - Polyhedron with least number of vertices whose …
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 …
Is there a $ (3,3)$-windmill graph with $19$ vertices?
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 …
Orientation of a geometric simplex - ordering of its vertices
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 …
geometry - Orientation of a triangle's vertices in 3D space: …
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 …
Online tool for making graphs (vertices and edges)?
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 …
combinatorics - Given a complete graph of $n$ vertices $K_n
Jan 12, 2016 · Given a complete graph of n vertices Kn K n (has all possible edges – one edge between pair of vertices). Use counting to find a formula in n n for the number of edges in the …
combinatorics - Every $k$ vertices in an $k$ - connected graph are ...
I have tried some ways - mainly using induction by removing one of the vertices of the set from the graph, and/or using Menger's theorem to construct the cycle. But I always encounter …
geometry - How many verticies, edges and faces (cells) does an nd ...
Mar 19, 2021 · So I guess a 1d hypercube is a line segment. It has 2 verticies and 1 edge. Not sure how many faces it has? A 2d hypercube is a square. It has 4 verticies and 4 edges. Again …