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- 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
- 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
- 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
- Find a non-trivial upper bound on the number of edges of a planar graph . . .
The degrees of the inner vertices $1$, $2$, $3$, and $4$ are $4$ and each of them is incident with the quadrilateral $1234$ We call this configuration a \emph {star}
- 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?
- Prove that if a graph has an Eulerian path, then the number of odd . . .
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 vertices must have even degrees If the number of odd-degree vertices is 0, then all vertices have even degrees, which is fine
- How to calculate the area of a 3D triangle?
I have coordinates of 3d triangle and I need to calculate its area I know how to do it in 2D, but don't know how to calculate area in 3d I have developed data as follows (119 91227722167969, 122
- Math Behind Creating a Perfect Star
0 The outer radius (of the outward pointing vertices) of a 5 pointed star divided by the inner radius (of the inward pointing vertices) = the golden ratio squared This is approximately 2 618 I discovered this while developing a procedure to draw a perfect star on a computer screen
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