duality in geometric graphs: vector graphs, kirchhoff graphs and maxwell reciprocal figures
Clicks: 131
ID: 233309
2016
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This
article has not been analysed, so there is no overall score —
reader engagement is measured and shown alongside.
Reader Engagement
Steady Performance
30.0
/100
131 views
32 readers
AI Quality Assessment
Not analyzed
Readership in this journal
SteadyRanked #58 of 89 articles by views in journal of hospitality and tourism management
Most read
Least read
Bar heights use a square-root scale.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
5
SUSD
one-off · no wallet required
Abstract
We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented by Fehribach, which can be defined independent of any matrix relations. In particular, we present simple cases in which vector graphs are guaranteed to be Kirchhoff or non-Kirchhoff. Next, we review Maxwell’s method of drawing reciprocal figures as he presented in 1864, using modern mathematical language. We then demonstrate cases in which R2-vector graphs defined from Maxwell reciprocals are “dual” Kirchhoff graphs. Given an example in which Maxwell’s theories are not sufficient to define vector graphs, we begin to explore other methods of developing dual Kirchhoff graphs.
| Reference Key |
reese2016symmetryduality
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | ;Tyler Reese;Randy Paffenroth;Joseph D. Fehribach |
| Journal | journal of hospitality and tourism management |
| Year | 2016 |
| DOI |
10.3390/sym8030009
|
| URL | |
| Keywords | Keywords not found |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.