9813

Isomorphic Types on Graphs: One-Neighborhood Gödel Sections

One-neighborhood isomorphic types can be sectioned into neighborhoods themselves. These neighborhoods of types can be uniquely numbered using a Gödel numbering scheme. Each section is a combination of a set of isomorphic types. This Demonstration is motivated to inspire further research on movements of sections on graphs during a graph rewriting evolution.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

These are the 209 one-neighbor isomorphic types with , numbered from left to right and top to bottom:
In the Demonstration, each vertex is labeled with the number of its one-neighbor isomorphic type. Then given a vertex, here called an anchor (shown in red), a neighborhood of the anchor is specified (shown in blue). The Gödel section number is calculated by tallying the number of isomorphic types and then building the value using the product of for each isomorphic type in the neighborhood, where is the prime, is the number of the isomorphic type, and is the tally.
I created this type of counting for graphs to help quantify and compare neighborhoods for my future research.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+