Abstract
A balanced 3-nearly Platonic graph of type (k, d) is a kregular planar graph with three faces of the same degree m, and all f − 3 remaining faces of degree d 6= m. We present constructions of infinite families of balanced 3-nearly Platonic graph of type (k, d) for all admissible pairs (k, d), whose existence was claimed by Deza, Dutour Sikirič, and Shtogrin in 2013.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 34-63 |
| Number of pages | 30 |
| Journal | Bulletin of the Institute of Combinatorics and its Applications |
| Volume | 86 |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019,Bulletin of the Institute of Combinatorics and its Applications.All Rights Reserved.
Keywords
- Planar graphs
- Platonic graphs
- regular graphs