Glossary

(Will be extended from time to time.)

connected

a net is connected, if there is a continous path from every vertex to every other vertex

embedding

a graph/net, in which the vertices have been assigned (eucledian) coordinates; this implies that now the edges have a certain length

graph

an abstract mathematical object in which vertices are connected by edges

k-connected

an k-connected graph is a graph in which k numbers of vertices (and their edges) have to be deleted to separate the graph into two parts

graphs, which consists of vertices which are all 3-coordinated can be indeed only 2-connected:

2-connected_graph

if the two orange vertices were deleted, the graph is disjoint

n-coordinated

an n-coordinated vertex has n connections to other vertices, n is the coordination number

shortform: n-c, for instance nbo is a 4-c net

if two or more vertices with different coordination numbers are present, the different coordination numbers of the vertices are separated by commas and are enclosed in brackets, for instance the net tbo is a (3,4)-c net

sometimes, a multinodal net is specified only in its short or compact form, i.e. only the different coordination numbers are given, in other cases every non-symmetry-related vertex is explicitely specified with its coordination number, for instance zhc is a octanodal (3,3,3,3,4,4,4,4)-c net; its short notation is again only (3,4)-c;

net

a finite or periodic, connected, and simple graph

simple means that the edges have no directions and that it contains no loops (edges linking a vertex to itself), and that there are no multiple edges between any vertices

quasiregular net

a quasiregular net is characterized by the transitivity pqrs = 1112

there is only one quasiregular net:
fcu

regular net

a regular net is characterized by the transitivity pqrs = 1111

there are only 5 regular nets:
bcu, dia, nbo, pcu, and srs

a regular net is vertex– as well as edge-transitive

semiregular net

a semiregular net is characterized by the transitivity pqrs = 11rs (with r > 1)

there are 16 semiregular nets:
lvt, sod, lcs, lcv, qtz, hxg, lcy, crs, bcs, acs, reo, thp, rhr, ana, ibb, and icc

a semiregular net is vertex– as well as edge-transitive

3 thoughts on “Glossary

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s