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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Dalibor Froncek
Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, Minnesota 55812, U.S.A
Electrical & Electronics Engineering

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On families of 2-nearly Platonic graphs Dalibor Froncek; Mahdi Reza Khorsandi; Seyed Reza Musawi; Jiangyi Qiu
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.23

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.
Co-Authors Jiangyi Qiu Mahdi Reza Khorsandi Seyed Reza Musawi