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 vertex and …
Proving that the number of vertices of odd degree in any graph G is ...
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 number of …
polyhedra - Polyhedron with least number of vertices whose diagonal ...
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 …
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 (for example, …
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 vertices, then we draw …
geometry - Orientation of a triangle's vertices in 3D space: Clockwise ...
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 $\vec {n}$, …
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 draw. …
combinatorics - Given a complete graph of $n$ vertices $K_n$ (has all ...
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 graph. I know …
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 problems with …
geometry - How many verticies, edges and faces (cells) does an nd ...
Mar 19, 2021 · Here are a couple hints. I will consider the vertices to be length- n n bitstrings. An edge connects two vertices if the vertices differ by a single bit flip. How many edges are incident to a given …