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p-Index From 2021 - 2026
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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Jiangyi Qiu
Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, U.S.A
Electrical & Electronics Engineering

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A note on nearly Platonic graphs with connectivity one Dalibor Froncek; Mahdi Reza Khorsandi; Seyed Reza Musawi; Jiangyi Qiu
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): 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.2021.9.1.17

Abstract

A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek, and Kreher on non-existence of 2-connected nearly Platonic graphs.
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 Dalibor Froncek Dalibor Froncek Mahdi Reza Khorsandi Seyed Reza Musawi