|
- 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 an edge are called incident, if the vertex is one of the two vertices the edge connects
- Is there a $ (3,3)$-windmill graph with $19$ vertices?
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, in case we do not fully trust the computer or GAP :)), the following representation is particularly convenient
- Show that a connected graph on $n$ vertices is a tree if and only if it . . .
Here's 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:
- Proving that the number of vertices of odd degree in any graph G is . . .
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 the number of edges
- geometry - Orientation of a triangles vertices in 3D space: Clockwise . . .
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 $\vec {n}$, $$\vec {n} = \left (\vec {v}_1 - \vec {v}_0\right)\times\left (\vec {v}_2 - \vec {v}_0\right) \tag {1}\label {1}$$ If we look along $\vec {n}$ in one direction, the vertices are clockwise; in the opposite
- 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 making sure that the cycle I'm building deosn't have repeating edges etc Help would be greatly appreciated :) Thanks!
- Online tool for making graphs (vertices and edges)?
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 (why do I have so many?
- How many nonisomorphic directed simple graphs are there with $n . . .
A directed simple graph is a structure consisting of the set of vertices and a binary relation that is irreflexive For the case of the disconnected graph, the relation is empty, and there is one such structure up to isomorphism for each different number of vertices The Wikipedia pages on graph theory are a good source if you are struggling with an unclear textbook
|
|
|