On families of 2-nearly Platonic graphs

Dalibor Froncek, Mahdi Reza Khorsandi, Seyed Reza Musawi, Jiangyi Qiu

Abstract


A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is called balanced if d1 = d2. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.

Keywords


Planar graphs; regular graphs; Platonic graphs

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DOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.23

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