Counting with Symmetry : Polya - Redfield Enumeration of Nonisomorphic Graphs
نویسنده
چکیده
Topology is the subfield of mathematics that is concerned with the study of shape. Mathematicians have studied topological questions for the past 250 years. However, in just the past 15 years topology has been found to have many different applications to real world problems. One of these is to use a topological tool called persistence homology to understand and analyze high dimensional and complex data sets. This talk will be an introduction to topology and the concept of homology. We will then use homology to a look at examples of how topological ideas can be used to give new and surprising insight towards understanding data.
منابع مشابه
On the Enumeration of Circulant Graphs of Prime Power and Square Free Orders
The aim of this work is twofold: to unify, systematize and extend the known results of the analytical (i.e. formula-wise) counting of directed and undirected circulant graphs with a prime or, more generally, square-free number of vertices; to develop a general combinatorial framework for the counting of nonisomorphic circulant graphs with pk vertices, p odd prime, k 2. The general problem of co...
متن کاملOn the Enumeration of One-Factorizations of Complete Graphs Containing Prescribed Automorphism Groups
In this paper we use orderly algorithms to enumerate (perfect) one-factorizations of complete graphs, the automorphism groups of which contain certain prescribed subgroups. We showed that, for the complete graph Ki2, excluding those one-factorizations containing exactly one automorphism of six disjoint cycles of length two, there are precisely 56391 nonisomorphic one-factorizations of Ki2 with ...
متن کاملTwo-factorizations of Small Complete Graphs Ii: the Case of 13 Vertices
We establish that for each of the 5005 possible types of 2factorizations of the complete graph K13, there exists at least one solution. We also enumerate all nonisomorphic solutions to the Oberwolfach problem
متن کاملThe Number of Locally Restricted Directed Graphs1
1. Preliminaries. We shall be concerned with finite graphs of / directed lines on n points, or nodes. The lines are joins from one point to another. To each point, Pi, is associated a non-negative number pair (r,-, st), where r{ is the number of lines from Pit and s; is the number of lines to P,. These number pairs are considered to be fixed local restrictions. Obviously, ]T),r,= ^,Sj=t. The ve...
متن کاملEquivalence classes of matchings and lattice-square designs
We enumerate nonisomorphic lattice-square designs yielded by a conventional construction. Constructed designs are speci3ed by words composed from 3nite-3eld elements. These words are permuted by the isomorphism group in question. The latter group contains a direct-product subgroup, acting, respectively, upon the positions and identities of the 3nite-3eld elements. We review enumeration theory f...
متن کامل