(New page: A graph is a thing made of point, some of which are linked by line segments. Generalize the idea to points that can also be grouped into triangles, or tetrahedra, etc. For graphs we know...) |
|||
| Line 1: | Line 1: | ||
| + | A simplicial complex is a special type of graph wherein the notion of a vertex is replaced with a new higher dimensional analog, called a simplex. | ||
| − | |||
| − | For graphs we know Euler's formula E+2=V+F. Give this a geometric meaning. | + | |
| + | ''A graph G = (V, E) consists of V, a nonempty set of vertices (or nodes) and E, a set of edges. Each edge has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints.''[[1]] | ||
| + | |||
| + | <br> A graph is a thing made of point, some of which are linked by line segments. Generalize the idea to points that can also be grouped into triangles, or tetrahedra, etc. | ||
| + | |||
| + | For graphs we know Euler's formula E+2=V+F. Give this a geometric meaning. | ||
Discuss (maybe in the 2-dimensional case) what might replace this formula compare a "triangulated" sphere to a "triangulated" doughnut. | Discuss (maybe in the 2-dimensional case) what might replace this formula compare a "triangulated" sphere to a "triangulated" doughnut. | ||
| − | [[2014 Spring MA 375 Walther|Back to MA375 Spring 2014]] | + | <br> |
| + | |||
| + | <br> | ||
| + | |||
| + | [[1]] Discrete Mathematics and Its Applications, Kenneth H. Rosen. [[2014 Spring MA 375 Walther|Back to MA375 Spring 2014]] | ||
[[Category:MA375Spring2014Walther]] [[Category:Math]] [[Category:Project]] | [[Category:MA375Spring2014Walther]] [[Category:Math]] [[Category:Project]] | ||
Revision as of 10:09, 27 April 2014
A simplicial complex is a special type of graph wherein the notion of a vertex is replaced with a new higher dimensional analog, called a simplex.
A graph G = (V, E) consists of V, a nonempty set of vertices (or nodes) and E, a set of edges. Each edge has either one or two vertices associated with it, called its endpoints. An edge is said to connect its endpoints.1
A graph is a thing made of point, some of which are linked by line segments. Generalize the idea to points that can also be grouped into triangles, or tetrahedra, etc.
For graphs we know Euler's formula E+2=V+F. Give this a geometric meaning.
Discuss (maybe in the 2-dimensional case) what might replace this formula compare a "triangulated" sphere to a "triangulated" doughnut.
1 Discrete Mathematics and Its Applications, Kenneth H. Rosen. Back to MA375 Spring 2014
